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This seminar covers a wide range of topics in Lie theory including (but not limited to) groups of Lie type, Lie algebras, Coxeter groups and their Hecke algebras, algebraic groups, and quantum groups, with emphasis on combinatorial and representation theoretic properties. Further information about upcoming seminars and people in the math department can be found at the CU Math Department Home Page.
Tue, Mar. 4 2:30pm (MATH 3…
Richard Green (CU)
X
We will show how to use root systems of types E6, E7, and E8 to construct generalizations of quantum Pfaffians and quantum Hafnians. These constructions are closely related to the combinatorics of del Pezzo surfaces, and they give rise to new q-analogues of an invariant cubic polynomial in type E6,and a quartic polynomial in type E7.
This is work in progress with Tianyuan Xu (University of Richmond).
Generalized quantum Pfaffians and quantum Hafnians
Tue, Apr. 8 2:30pm (MATH 3…
Shigenori Nakatsuka (FAU Erlangen-Nurnberg)
X
W-superalgebras are a large class of vertex algebras obtained from affine Lie algebras. Due to their duality, hook-type W-superalgebras have captured a lot of attention in the last decade. I will explain the duality in their representation theory and the phenomenon appearing at the level of characters.
Duality of hook-type W-superalgebras and characters Sponsored by the Meyer Fund
Tue, Apr. 15 2:30pm (MATH 3…
Gurbir Dhillon (UCLA)
X
The representation theory of affine Lie algebras in characteristic zero has been well studied for over fifty years, and has rich connections with algebraic geometry, mathematical physics, and number theory. By contrast, in positive characteristic, much less is known. In the talk, I will review some earlier results in this area, and state some new ones, namely the determination of the Harish--Chandra center and the linkage principle for highest weight representations at all levels. Time permitting, we will discuss some further conjectures. This is based on joint work in progress with Ivan Loseu.
Representations of affine Lie algebras in positive characteristic
Tue, Apr. 22 2:30pm (MATH 3…
Juan Villarreal (University of Colorado Boulder)
X
In this talk, we will show how to associate certain varieties to algebras and modules, called associated varieties. Then, we will explain how some geometric properties of these varieties have deep implications in representation theory. Finally, we will explain how some of these relations also holds in infinite dimensions.
Generalized quantum Pfaffians and quantum Hafnians