TY - JOUR
TI - Spectral functions of invariant operators on skew multiplicity free spaces
DO - https://doi.org/doi:10.7282/T3N016FP
PY - 2007
AB - This thesis extends results on spectral functions of invariant differential operators on multiplicity free spaces to the setting of skew multiplicity free spaces, which are representations of a reductive group whose exterior algebra decomposes into a direct sum of pairwise nonisomorphic irreducibles. We prove in the general skew multiplicity free case that the spectral functions satisfy a vanishing property and a transposition formula which are formally identical to those satisfied by their multiplicity free analogues. We investigate two special cases, the GL_nC modules S^2C^n and Wedge^2 C^n, for which the spectral functions of invariant operators form a family of supersymmetric functions which can be identified with the factorial Schur Q functions. From this equivalence we deduce several properties of each family, giving the spectral functions a combinatorial interpretation and the factorial Schur Q functions a new representation theoretic one.
KW - Mathematics
KW - Differential operators
KW - Skew fields
KW - Combinatorial analysis
LA - eng
ER -