A quotient of the affine Hecke algebra in the Brauer algebra. (English) Zbl 0852.20035

Jones, V. F. R.

Enseign. Math., II. Sér. 40, No. 3-4, 313-344 (1994).

Summary: The structure of a certain subalgebra of Brauer’s centralizer algebra is given for all values of the parameter for which it is semisimple. The algebra admits a trace functional whose weights on the simple components of the algebra are calculated. The algebra may be exhibited as a quotient of the affine Hecke algebra of type \(\widetilde A_n\), using generators and relations.

MSC:

20G05	Representation theory for linear algebraic groups
16P10	Finite rings and finite-dimensional associative algebras
20C30	Representations of finite symmetric groups
16W30	Hopf algebras (associative rings and algebras) (MSC2000)

Keywords:

Brauer’s centralizer algebras; trace functionals; simple components; affine Hecke algebras; generators; relations