A Note on Weyl Modules for _∞ and _∞

Abstract

In this article we extend Jantzen's formula for the determinant of the contravariant form on highest weight   _n -modules to a formula for highest weight   _∞-modules. This, in turn, has applications to the representation theory of (degenerate and nondegenerate) cyclotomic Hecke algebras.

Key Words:

• Shapovalov form

Mathematics Subject Classification:

• 17B67
• 20C08

Notes

Communicated by D. K. Nakano.