Speaker: Tamar Seeman (Weizmann Institute)

Title: "The module decomposition of super-symmetric powers of matrices"

Abstract:
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Let M be the k x m matrices over C. The GL(k) x GL(m) decompositions of 
the symmetric and exterior powers of M are described by two classical 
theorems. In an earlier talk I discussed a theorem for Lie super-algebras
which implies both classical theorems as special cases. That super-algebra
theorem generalizes to a class of algebras defined by partitions.

Let M^+ and M^- be the symmetric and skew symmetric k x k matrices. In 
this talk I present a second theorem for Lie super-algebras which gives
the GL(k) decompositions of the symmetric powers of M^+ and M^- as 
special cases.

Both of these super-theorems are reflected combinatorially in bijections
due to Remmel involving super semistandard Young tableaux.