Basic Information

Faculty

• 理学部

Professional Memberships

• 数学会

Academic Degree

• 修士（理学）(京都大学)
• 博士（理学）(京都大学)

Academic Resume (Graduate Schools)

• 京都大学, 大学院理学研究科博士後期課程数学専攻, 修了
• 京都大学, 大学院理学研究科修士課程数学専攻, 修了

Academic Resume (Undergraduate School/Majors)

• 京都大学, 理学部, 卒業

Language of Instruction

• English

ID,URL

• J-Global ID

  200901019248476533

Website(s) (URL(s))

• http://www.math.kyoto-u.ac.jp/~kikuchi/

researchmap URL

• https://researchmap.jp/read0046928

Research

Research Topics, Overview of the research

• Research Topics

  Functional analysis, Harmonic analysis on Lie groups and on their homogeneous spaces, Unitary representations of Solvable Lie groups,
  Multiplicity-free actions

• Overview of the research

  I am interested in harmonic analysis on solvable Lie groups and on their compact extensions. Most interested objects are Gelfand pairs and the corresponding homogeneous spaces. In order to analyze them, I study spherical representations and spherical functions. Constructions of spherical representations for Gelfand pairs and calculations of invariant differential operators for multiplicity-free actions are very useful for the investigations of them.
  

Research Interests

• 基礎解析学
• Basic Analysis

Research Areas

• Natural sciences, Basic analysis

Papers

• Spherical representations for certain Gelfand pairs (Development of Representation Theory and its Related Fields)

  Kikuchi Katsuhiko

  RIMS Kokyuroku, Feb. 2014

  Access this paper :

  
• Invariant Polynomials for Multiplicity-free Actions of Rank Four (New Viewpoints of Representation Theory and Noncommutative Harmonic Analysis)

  KIKUCHI KATSUHIKO

  RIMS Kokyuroku Bessatsu, Oct. 2010, Peer-reviewed

  
• Invariant polynomials and invariant differential operators for multiplicity-free actions of rank three (Representation Theory and Analysis on Homogeneous Spaces)

  Kikuchi Katsuhiko

  RIMS Kokyuroku Bessatsu, Apr. 2008, Peer-reviewed

  
• On a classification of Gelfand pairs (Representation theory and harmonic analysis on homogeneous spaces)

  Kikuchi Katsuhiko

  RIMS Kokyuroku, Jan. 2005

  Access this paper :

  
• Remarks on Gelfand pairs associated to non-type-I solvable Lie groups

  K Kikuchi

  JOURNAL OF FUNCTIONAL ANALYSIS, Dec. 1998, Peer-reviewed

  
• K-spherical representations for Gelfand pairs associated to solvable Lie groups

  Katsuhiko Kikuchi

  Journal of the Mathematical Society of Japan, 1997, Peer-reviewed

  
• 可解リー群上のK-球函数の正定値性(等質空間上の非可換解析学)

  菊地 克彦

  数理解析研究所講究録, Jan. 1995

  
• ON GELFAND PAIRS ASSOCIATED WITH NILPOTENT LIE-GROUPS

  KIKUCHI, K

  JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, Dec. 1994, Peer-reviewed

  
• 巾零リー群に付随するゲルファント対(リー群の構造と表現に関する諸問題)

  菊地 克彦

  数理解析研究所講究録, Dec. 1993

  

Misc.

• Invariant differential operators for multiplicity-free actions

  Katsuhiko Kikuchi

  Sugaku, Apr. 2024, Peer-reviewed, Lead author

  
• あるGelfand対の球表現

  菊地 克彦

  京都大学数理解析研究所講究録, 2014

  
• Gelfand対の分類について

  菊地 克彦

  京都大学数理解析研究所講究録, 2005

  
• K-spherical representations for Gelfand pairs associated to solvable Lie groups

  K Kikuchi

  JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, Jul. 1997

  
• Jordan triple systems and K-spherical functions on Heisenberg

  Symposium on Representation Theory, 1996

  
• Jordan trple systems and $K$-spherical functions on Heisenberg groups

  KIKUCHI Katsuhiko

  平成8年度表現論シンポジウム講演集, 1996

  
• 可解リー群上のK-球函数の正定値性

  京都大学数理解析研究所講究録, 1995

  
• Positive definiteness of K-spherical functions on solvable Lie groups

  1995

  
• ON GELFAND PAIRS ASSOCIATED WITH NILPOTENT LIE-GROUPS

  K KIKUCHI

  JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, Dec. 1994

  
• 巾零リー群に付随するゲルファント対

  京都大学数理解析研究所講究録, 1993

  
• On Gelfand pairs associated with nilpotent Lie groups

  1993

  
• Remarks on Gelfand pairs associated to non type I solvable Lie groups

  Journal of Functional Analysis

  

Presentations

• あるGelfand対に対する球表現

  菊地 克彦

  日本数学会秋季総合分科会(愛媛大学), Sep. 2013

  
• 階数4の半古典型multiplicity-free作用に関する不変微分作用素

  菊地 克彦

  日本数学会秋季総合分科会(東京大学), Mar. 2009

  
• ${\rm{Sp } }(n)$の可約なmultiplicity-free作用に関する不変式と不変微分作用素

  菊地 克彦; 反橋 拓朗

  日本数学会秋季総合分科会(東京工業大学), Sep. 2008

  
• 階数3のmultiplicity-free空間上の不変式と不変微分作用素

  菊地 克彦

  日本数学会秋季総合分科会(大阪市立大学), Sep. 2006

  
• 冪零Lie群に付随するGelfand対の分類について

  菊地 克彦

  日本数学会秋季総合分科会(北海道大学), Sep. 2004

  
• Heisenberg群上の$K$-球函数

  菊地 克彦

  日本数学会年会(信州大学), Mar. 1997

  
• 非I型可解Lie群に付随するGelfand対

  菊地 克彦

  日本数学会秋季総合分科会(東京都立大学), Sep. 1996

  
• 可解リー群上のK-球函数の正定値性

  菊地 克彦

  日本数学会秋季総合分科会(東京工業大学), Sep. 1994

  
• 巾零Lie群に付随するGelfand対

  菊地 克彦

  日本数学会秋季総合分科会(大阪府立大学), Sep. 1993

  

External funds: Kakenhi

• global problems on non-commutative algebraic geometry

  Grant-in-Aid for Scientific Research (C)

  Kochi University

  Yoshifumi Tsuchimoto

  From 01 Apr. 2012, To 31 Mar. 2017, Project Closed

  非可換代数幾何学;非可換環論;ワイル環;ジャコビアン問題;非可換代数多様体;非可換射影多様体;ドルボー複体;Deligne-Illusie 理論;非可換ケーラー多様体;ケーラー多様体;非可換幾何学;射影多様体;力学系;有限体;ゼータ関数;Jacobian 問題;Dixmier 予想;多項式力学系

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-24540044/
• Studies on global problems on non commutative algebraic geometry

  Grant-in-Aid for Scientific Research (C)

  Kochi University

  Tsuchimoto YOSHIFUMI;Yoshifumi TSUCHIMOTO

  From 01 Apr. 2008, To 31 Mar. 2012, Project Closed

  非可換代数幾何学;射影幾何学;射影的加群;Dixmier予想;Jacobian問題;反射的加群;Jacobian予想;シンプレクティック構造;Moyal積;Dixmier問題;dixmier予想

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540046/
• Orbit correspondence on flag manifolds and integral transformations

  Grant-in-Aid for Scientific Research (C)

  Kyoto University

  Toshihiko MATSUKI

  From 01 Apr. 2007, To 31 Mar. 2010, Project Closed

  対称空間;リー群;表現論

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540076/
• Affine quotient maps and invariant differential operators

  Grant-in-Aid for Scientific Research (B)

  Kyoto University

  Kyo NISHIYAMA

  From 01 Apr. 2005, To 31 Mar. 2009, Project Closed

  アフィン商多様体;不変式論;ユニタリ表現;冪零軌道;旗多様体;モーメント写像;隨伴多様体;dual pair;退化主系列表現;Capelli恒等式;Weil表現;不変微分作用素;特異点解消;随伴サイクル;カペリ恒等式;概均質ベクトル空間

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17340037/
• Representation Theory and Duality associated with Non-commutative Special Functions

  Grant-in-Aid for Scientific Research (B)

  Kyoto University

  Toru UMEDA

  From 01 Apr. 2004, To 31 Mar. 2008, Project Closed

  特殊函数;Capelli恒等式;dual pair;双対性;普遍包絡環;不変式論;超幾何;二項型多項式;Dual pair;対称式, spacial functions;Capelli identities;dual pair;duality;universal enveloping algebra;invariant theory;hypergeometric functions;polynomials of binomial type

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340039/
• Geometric harmonic analysis on homogeneous Siegel domains

  Grant-in-Aid for Scientific Research (B)

  KYUSHU UNIVERSITY;Kyoto University

  Takaaki NOMURA

  From 01 Apr. 2002, To 31 Mar. 2006, Project Closed

  ジーゲル領域;ケーリー変換;擬逆元写像;正規j代数;等質錐;対称錐;管状領域;ジョルダン代数;等質錘;対称錘;分裂可解リー群;ポアッソン核;ラプラシアン;有界等質領域;非可換調和解析, Siegel domain;Cayley transform;pseudoinverse map;normal j-algebra;homogenous cone;symmetric cone;tube domain;Jordan algebra

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14340044/
• 可解リー群上の調和解析の新展開

  Grant-in-Aid for Exploratory Research

  Kyoto University

  野村 隆昭

  From 01 Apr. 2000, To 31 Mar. 2002, Project Closed

  ジーケル領域;等質錐;分裂可解リー群;ポアッソン核;ラプラシアン;ケーリー変換;有界等質領域;非可換調和解析;ジーゲル領域;ベレジン変換

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12874020/
• 非I型群とそのコンパクト拡大上の調和解析

  Grant-in-Aid for Encouragement of Young Scientists (A)

  Kyoto University

  菊地 克彦

  From 01 Apr. 1999, To 31 Mar. 2000, Project Closed

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11740089/
• Study of special functions based on representation and invariant theories

  Grant-in-Aid for Scientific Research (B)

  KYOTO UNIVERSITY

  Toru UMEDA

  From 01 Apr. 1999, To 31 Mar. 2002, Project Closed

  特殊函数;表現論;不変式論;不変微分作用素;Capelli恒等式;超幾何函数;行列式;パフィアン;群の表現;不変式;群行列式;Lie環;不偏包絡環;Poincare Birkhoff-Wittの定理;対称群;量子群;リー環;普遍包絡環;球函数;パーマネント;Wronski関係式;五角数定理, special functions;representation theory;invariant theory;invariant differential operations;Copelli identity;hypergeometric functions;determinant;Pfaphan

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11440043/
• 可解リー群とそのコンパクト拡大上の調和解析

  Grant-in-Aid for Encouragement of Young Scientists (A)

  Kyoto University

  菊地 克彦

  From 01 Apr. 1997, To 31 Mar. 1999, Project Closed

  可解リー群;調和解析;球函数

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09740100/
• Studies on the theory of representations of groups and algebras

  Grant-in-Aid for Scientific Research (A)

  KYOTO UNIVERSITY

  Takeshi HIRAI

  From 01 Apr. 1997, To 31 Mar. 1999, Project Closed

  群の表現;環の表現;半単純リー群の表現;表現論;無限次元群の表現論;無限次元環の表現;数論;確率過程;量子情報理論;無限次元均質空間上;調和解析, representations of groups;representations of algebras;representations of semisimple Lie groups

  https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09304015/

Education

Teaching subject(s)

• From 01 Apr. 2025, To 31 Mar. 2026

  Calculus with Exercises B

  N150, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2025, To 31 Mar. 2026

  Calculus with Exercises A

  N149, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  How to write mathematical papers

  0067, Spring, Graduate School of Science, 1
• From 01 Apr. 2024, To 31 Mar. 2025

  Special study course (Mathematical Science)

  5140, Year-long, Faculty of Science, 12
• From 01 Apr. 2024, To 31 Mar. 2025

  Calculus with Exercises A

  N149, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Linear Algebra with Exercises A

  N151, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2024, To 31 Mar. 2025

  Calculus with Exercises B

  N150, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  How to write mathematical papers

  0067, Spring, Graduate School of Science, 1
• From 01 Apr. 2023, To 31 Mar. 2024

  Special study course (Mathematical Science)

  5140, Year-long, Faculty of Science, 12
• From 01 Apr. 2023, To 31 Mar. 2024

  Linear Algebra with Exercises A

  N151, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Calculus with Exercises B

  N150, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2023, To 31 Mar. 2024

  Calculus with Exercises A

  N149, Spring, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Calculus with Exercises B

  N150, Fall, Institute for Liberal Arts and Sciences, 3
• From 01 Apr. 2022, To 31 Mar. 2023

  Calculus with Exercises A

  N149, Spring, Institute for Liberal Arts and Sciences, 3
• From Apr. 2021, To Mar. 2022

  Calculus with Exercises B

  Fall, 全学共通科目
• From Apr. 2021, To Mar. 2022

  Calculus with Exercises A

  Spring, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Calculus with Exercises B

  Fall, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Seminar on Analysis d

  Fall, 理学研究科
• From Apr. 2020, To Mar. 2021

  Linear Algebra with Exercises B

  Fall, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Calculus with Exercises A

  Spring, 全学共通科目
• From Apr. 2020, To Mar. 2021

  Seminar on Analysis c

  Spring, 理学研究科
• From Apr. 2020, To Mar. 2021

  Linear Algebra with Exercises A

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Calculus with Exercises B

  Fall, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Linear Algebra with Exercises B

  Fall, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Advanced Calculus I - Vector Calculus

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Calculus with Exercises A

  Spring, 全学共通科目
• From Apr. 2019, To Mar. 2020

  Linear Algebra with Exercises A

  Spring, 全学共通科目
• From Apr. 2018, To Mar. 2019

  Calculus with Exercises B

  Fall, 全学共通科目
• From Apr. 2018, To Mar. 2019

  Mathematical Statistics

  Fall, 全学共通科目
• From Apr. 2018, To Mar. 2019

  Calculus with Exercises A

  Spring, 全学共通科目
• From Apr. 2018, To Mar. 2019

  Mathematics seminary

  Year-long, 理学部
• From Apr. 2017, To Mar. 2018

  Seminar on Analysis D

  Fall, 理学研究科
• From Apr. 2017, To Mar. 2018

  Mathematical Statistics

  Fall, 全学共通科目
• From Apr. 2017, To Mar. 2018

  Linear Algebra with Exercises B

  Fall, 全学共通科目
• From Apr. 2017, To Mar. 2018

  Seminar on Analysis C

  Spring, 理学研究科
• From Apr. 2017, To Mar. 2018

  Linear Algebra with Exercises A

  Spring, 全学共通科目
• From Apr. 2016, To Mar. 2017

  Calculus with Exercises B

  Fall, 全学共通科目
• From Apr. 2016, To Mar. 2017

  Seminar on Analysis B

  Fall, 理学研究科
• From Apr. 2016, To Mar. 2017

  Linear Algebra with Exercises B

  Fall, 全学共通科目
• From Apr. 2016, To Mar. 2017

  Calculus with Exercises A

  Spring, 全学共通科目
• From Apr. 2016, To Mar. 2017

  Seminar on Analysis A

  Spring, 理学研究科
• From Apr. 2016, To Mar. 2017

  Linear Algebra with Exercises A

  Spring, 全学共通科目
• From Apr. 2016, To Mar. 2017

  Mathematics seminary

  Year-long, 理学部
• From Apr. 2015, To Mar. 2016

  Advanced Calculus II - Differential Equations

  Fall, 全学共通科目
• From Apr. 2015, To Mar. 2016

  Seminar on Analysis D

  Fall, 理学研究科
• From Apr. 2015, To Mar. 2016

  Exercises in Analysis II

  Fall, 理学部
• From Apr. 2015, To Mar. 2016

  Advanced Calculus I - Vector Calculus

  Spring, 全学共通科目
• From Apr. 2015, To Mar. 2016

  Seminar on Analysis C

  Spring, 理学研究科
• From Apr. 2015, To Mar. 2016

  Mathematics seminary

  Year-long, 理学部
• From Apr. 2014, To Mar. 2015

  Seminar on Analysis B

  Fall, 理学研究科
• From Apr. 2014, To Mar. 2015

  Linear Algebra A

  Fall, 全学共通科目
• From Apr. 2014, To Mar. 2015

  Basic Mathematics IIB

  Fall, 全学共通科目
• From Apr. 2014, To Mar. 2015

  Exercises of Linear Algebra A

  Spring, 理学部
• From Apr. 2014, To Mar. 2015

  Seminar on Analysis A

  Spring, 理学研究科
• From Apr. 2014, To Mar. 2015

  Basic Mathematics IIA

  Spring, 全学共通科目
• From Apr. 2013, To Mar. 2014

  Seminar on Analysis D

  Fall, 理学研究科
• From Apr. 2013, To Mar. 2014

  Calculus B

  Fall, 全学共通科目
• From Apr. 2013, To Mar. 2014

  Exercises of Linear Algebra A

  Spring, 理学部
• From Apr. 2013, To Mar. 2014

  Exercisesd Advanced Calculus I

  Spring, 理学部
• From Apr. 2013, To Mar. 2014

  Seminar on Analysis C

  Spring, 理学研究科
• From Apr. 2012, To Mar. 2013

  Exercises of Linear Algebra B

  Fall, 理学部
• From Apr. 2012, To Mar. 2013

  Seminar on Analysis B

  Fall, 理学研究科
• From Apr. 2012, To Mar. 2013

  Linear Algebra B

  Fall, 全学共通科目
• From Apr. 2012, To Mar. 2013

  Seminar on Analysis A

  Spring, 理学研究科
• From Apr. 2012, To Mar. 2013

  Linear Algebra A

  Spring, 全学共通科目
• From Apr. 2011, To Mar. 2012

  Linear Algebra A

  Fall, 全学共通科目
• From Apr. 2011, To Mar. 2012

  Linear Algebra B

  Fall, 全学共通科目
• From Apr. 2011, To Mar. 2012

  数学基礎演習II

  Fall, 理学部
• From Apr. 2011, To Mar. 2012

  Linear Algebra A

  Spring, 全学共通科目
• From Apr. 2011, To Mar. 2012

  数学講究

  Year-long, 理学部

Administration

Faculty management (title, position)

• From 01 Apr. 2019, To 31 Mar. 2021

  理学研究科セミナーハウス管理運営委員会委員