928 research outputs found
An Analysis of the Multiplicity Spaces in Branching of Symplectic Groups
Branching of symplectic groups is not multiplicity-free. We describe a new
approach to resolving these multiplicities that is based on studying the
associated branching algebra . The algebra is a graded algebra whose
components encode the multiplicities of irreducible representations of
in irreducible representations of . Our first theorem
states that the map taking an element of to its principal submatrix induces an isomorphism of \B to a different branching
algebra \B'. The algebra \B' encodes multiplicities of irreducible
representations of in certain irreducible representations of
. Our second theorem is that each multiplicity space that arises in
the restriction of an irreducible representation of to is
canonically an irreducible module for the -fold product of . In
particular, this induces a canonical decomposition of the multiplicity spaces
into one dimensional spaces, thereby resolving the multiplicities.Comment: 32 pages, revised abstract and introduction, and reorganized the
structure of the pape
Quantum Polynomial Functors
We construct a category of quantum polynomial functors which deforms
Friedlander and Suslin's category of strict polynomial functors. The main aim
of this paper is to develop from first principles the basic structural
properties of this category (duality, projective generators, braiding etc.) in
analogy with classical strict polynomial functors. We then apply the work of
Hashimoto and Hayashi in this context to construct quantum Schur/Weyl functors,
and use this to provide new and easy derivations of quantum
duality, along with other results in quantum invariant theory.Comment: 34 pages, final version to appear in Journal of Algebr
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