nLab
asymptotic representation theory
Contents
Context
Representation theory
representation theory

geometric representation theory

Ingredients
representation , 2-representation , ∞-representation

group , ∞-group

group algebra , algebraic group , Lie algebra

vector space , n-vector space

affine space , symplectic vector space

action , ∞-action

module , equivariant object

bimodule , Morita equivalence

induced representation , Frobenius reciprocity

Hilbert space , Banach space , Fourier transform , functional analysis

orbit , coadjoint orbit , Killing form

unitary representation

geometric quantization , coherent state

socle , quiver

module algebra , comodule algebra , Hopf action , measuring

Geometric representation theory
D-module , perverse sheaf ,

Grothendieck group , lambda-ring , symmetric function , formal group

principal bundle , torsor , vector bundle , Atiyah Lie algebroid

geometric function theory , groupoidification

Eilenberg-Moore category , algebra over an operad , actegory , crossed module

reconstruction theorems

Measure and probability theory
Contents
Idea
Asymptotic representation theory is representation theory in the limit of large dimension of linear representation and/or of large groups being represented.

Much of asymptotic representation theory is concerned specifically with the symmetric group and studies asymptotics of shapes of Young diagrams and of numbers of Young tableaux under measures such as the Plancherel measure and/or the Schur-Weyl measure .

References
Anatoly Vershik , Two lectures on the asymptotic representation theory and statistics of Young diagrams , In: Vershik A.M., Yakubovich Y. (eds) Asymptotic Combinatorics with Applications to Mathematical Physics Lecture Notes in Mathematics, vol 1815. Springer 2003 (doi:10.1007/3-540-44890-X_7 )

G. Olshanski , Asymptotic representation theory , Lecture notes 2009-2010 (webpage , pdf 1 , pdf 2 )

Piotr Śniady, Combinatorics of asymptotic representation theory , European Congress of Mathematics 2012 (arXiv:1203.6509 )

Created on June 3, 2021 at 07:25:08.
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