Abstract for the talk on 20.03.2018 (11:00 h)Seminar on Nonlinear Algebra
Cédric Lecouvey (Université François Rabelais, Tours)
Combinatorics of Generalized exponents
Generalized exponents are important graded multiplicities in representation theory of simple Lie algebras. Notably, they are particular Kazhdan-Lusztig polynomials. In type A, they admit a nice combinatorial description in terms of Lascoux-Schützenberger’s charge statistics on semistandard tableaux. In this talk I will recall their definition and explain how to get similar statistics beyond type A. This will give a combinatorial proof of the positivity of their coefficients but also some other interesting properties. This is a work in collaboration with Cristian Lenart.