Classical affine algebras

Higher Level Young Walls for Classical Quantum Affine Algebras

Deformed Universal Characters for Classical and Affine Algebras

Creation operators are given for the three distinguished bases of the type BCD universal character ring of Koike and Terada yielding an elegant way of treating computations for all three types in a unified manner. Deformed versions of these operators create symmetric function bases whose expansion in the universal character basis, has polynomial coefficients in q with non-negative integer coeff...

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

Symplectic Reflection Algebras and Affine Lie Algebras

These are the notes of my talk at the conference “Double affine Hecke algebras and algebraic geometry” (MIT, May 18, 2010). The goal of this talk is to discuss some results and conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the representation theory for affine Lie algebras. These conjectures arose fr...

Cluster algebras and quantum affine algebras

Let C be the category of finite-dimensional representations of a quantum affine algebra Uq(ĝ) of simply-laced type. We introduce certain monoidal subcategories Cl (l ∈ N) of C and we study their Grothendieck rings using cluster algebras.