New Realization of Cyclotomic -Schur Algebras

  • Kentaro Wada

    Shinshu University, Matsumoto, Japan

Abstract

We introduce a Lie algebra and an associative algebra associated with the Cartan data of which is separated into parts with respect to such that . We show that the Lie algebra is a filtered deformation of the current Lie algebra of , and we can regard the algebra as a \lq\lq -analogue" of . Then, we realize a cyclotomic -Schur algebra as a quotient algebra of under a certain mild condition. We also study the representation theory for and , and we apply them to the representations of the cyclotomic -Schur algebras.

Cite this article

Kentaro Wada, New Realization of Cyclotomic -Schur Algebras. Publ. Res. Inst. Math. Sci. 52 (2016), no. 4, pp. 497–555

DOI 10.4171/PRIMS/188