Jun Hu (Beijing Institute of Technology)

Friday 18th August, 12.05-12.55pm, Carslaw 373

Crystal bases and simple modules for the cyclotomic Hecke algebra of type G(r,p,n)

In this talk, I shall review the recent progress on the modular representations of the cyclotomic Hecke algebra of type G(r,p,n). The crystal bases theory of Fock spaces over certain quantum affine algebras is applied to the modular representations of these cyclotomic Hecke algebras. This yields classification of simple modules over these cyclotomic Hecke algebras. Furthermore, using Naito-Sagaki's work [S. Naito & D. Sagaki, J. Algebra 251 (2002) 461--474] on Lakshmibai-Seshadri paths fixed by diagram automorphisms, we obtain explicit formulas for the number of simple modules over these cyclotomic Hecke algebras.