The Białynicki-Birula--Hochschild--Mostow theory of rational representative functions (AGC Seminar)
- Event Type
- Seminar/Symposium
- Sponsor
- Algebra, Geometry, Combinatorics Seminar
- Location
- 3217 Everitt
- Date
- Sep 21, 2023 3:00 - 3:50 pm
- Speaker
- William Haboush (UIUC)
- Contact
- Alexander Yong
- ayong@illinois.edu
- Views
- 40
- Originating Calendar
- Algebra, Geometry, and Combinatorics Seminar
I will give an exposition of a celebrated series of papers by the three referenced authors. They proved that if G is a semisimple algebraic group over a field of characteristic 0 and if {I_λ : λ ∈ Λ} is a set of representatives of the isomorphism classes of irreducible representations of G then the coordinate ring of G is the direct sum k[G] = \bigoplus_{λ∈Λ} I_λ ⊗k I*_λ. The proof uses mostly elementary notions such as the left and right translation actions on k[G] and the notion of the matrix coefficients of an algebraic representation.