Induced representations and traces for chains of affine and cyclotomic Hecke algebras

Abstract

Properties of relative traces and symmetrizing forms on chains of cyclotomic and affine Hecke algebras are studied. The study relies on a use of bases of these algebras which generalize a normal form for elements of the complex reflection groups $G(m,1,n)$, $m=1,2,\dots ,\infty$, constructed by a recursive use of the Coxeter--Todd algorithm. Formulas for inducing, from representations of an algebra in the chain, representations of the next member of the chain are presented.

References in corpus (1)

• Knot theory related to generalized and cyclotomic Hecke algebras of type B

Cited by in corpus (4)

• Cyclotomic Yokonuma-Hecke algebras are cyclotomic quiver Hecke algebras
• Markov traces on affine and cyclotomic Yokonuma-Hecke algebras
• Fusion procedure for the walled Brauer algebra
• Cyclotomic shuffles