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Representation Theory and Harmonic Analysis Lab
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A research field that studies, from various standpoints, what is invariant on a set acted on by groups and similar structures.
AboutAbout the lab
Studying what stays invariant under an action, from many standpoints
The Representation Theory and Harmonic Analysis field studies sets on which algebraic structures such as groups act, focusing on objects that are invariant under the action as well as objects that are analogous to invariants.
When the set consists of functions, the field connects with analysis, and when it has a geometric structure, it connects with geometry as well.
It is a field that can be approached not only through algebra but also from many other standpoints.
Faculty members of the Faculty of Mathematics, the Institute of Mathematics for Industry, and the Faculty of Arts and Science are part of this field.
Key terms
- Action
- The way an element of an algebraic structure such as a group moves a point of a set to another point
- Invariant
- Remaining unchanged when the action is applied. This field studies what is invariant
- Branching law
- The problem of determining how a representation of a group behaves when restricted to a subgroup
ResearchResearch themes
When an algebraic structure such as a group acts on a set, this field studies what is invariant under the action, as well as objects that are analogous to invariants. In addition to algebra, it connects with analysis when the set consists of functions, and with geometry when the set has a geometric structure.
*Illustrative imageStudying What Is Invariant Under an Action
The field studies sets on which algebraic structures such as groups act, focusing on objects that are invariant under the action and objects that are analogous to them. It connects with analysis when the set consists of functions, and with geometry when the set has a geometric structure.
*Illustrative imageAutomorphic Forms and Representation Theory
Associate Professor Takuya Konno works on number-theoretic studies of automorphic forms. From the representation theory side, the research examines the Arthur-Selberg trace formula, the representation theory of reductive groups over p-adic fields, and endoscopy.
*Illustrative imageBranching Laws for Representations of Lie Groups
Associate Professor Masatoshi Kitagawa studies branching laws, the problem of how a representation of a group behaves when restricted to a subgroup. The research examines conditions under which the modules appearing in branching laws of reductive Lie algebras are irreducible, as well as properties of large modules used for branching problems.
*Illustrative imageRepresentation Theory of Rings and Homological Algebra
Assistant Professor Norihiro Hanihara studies the representation theory of rings. The research examines the homological algebraic structures that appear in the Cohen-Macaulay representation theory of finite-dimensional algebras and commutative Gorenstein rings, using triangulated categories such as derived categories and their enhancements by differential graded categories.
MembersFaculty
- ProfessorLin Weng
- ProfessorHiroyuki Ochiai
- ProfessorYasuro Gon
- ProfessorRyoko Tomiyasu
- Associate ProfessorMasatoshi Kitagawa
- Associate ProfessorTakuya Konno
- Associate ProfessorYosuke Morita
- Assistant ProfessorNorihiro Hanihara
- Assistant ProfessorRyo Yamagishi
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Worm's-eye view of Tokyo Skytree with vertical symmetry impression, a sunny day, in Japan” Basile Morin / CC BY-SA 4.0 (cropped)
- Studying What Is Invariant Under an Action: “Rubik's cube, CN II” kaʁstn Disk/Cat / CC BY-SA 3.0 (cropped)
- Automorphic Forms and Representation Theory: “Representation of SU(3)” Arkadipta Sarkar at English Wikipedia / CC BY-SA 3.0 (cropped)
- Branching Laws for Representations of Lie Groups: “Weights for A2 root system” Mathphysman / CC BY-SA 4.0 (cropped)
- Representation Theory of Rings and Homological Algebra: “Constantsheaf intermediate step” Jakob.scholbach (talk) / Public domain (cropped)
- Related lab (Topology Lab): “Klein bottle green” Aizenr / CC BY-SA 4.0 (cropped)
- Related lab (Operator Theory and Operator Algebras Lab): “Commutative Diagram 2” Yoelpiccolo31 / CC BY-SA 4.0 (cropped)
- Related lab (Algebraic Geometry Lab): “Heike Kamerlingh Onnes - 29 - Plaster model of a Ψ surface of a mixture of two substances” 作者不詳 / Public domain (cropped)
- Related lab (Number Theory Lab): “SinRiemannSiegelTheta” Chrgue / CC BY-SA 3.0 (cropped)
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