Cellular algebras arising from Hecke algebras of type H-n

摘要

We study a finite-dimensional quotient of the Hecke algebra of type H-n for general n, using a calculus of diagrams. This provides a basis of monomials in a certain set of generators. Using this, we prove a conjecture of C.K. Fan about the semisimplicity of the quotient algebra. We also discuss the cellular structure of the algebra, with certain restrictions on the ground ring. [References: 13]