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An Elliptic Hypergeometric Function Approach to Branching Rules
Chul-hee Lee, Eric M. Rains, S. Ole Warnaar
We prove Macdonald-type deformations of a number of well-known classical branching rules by employing identities for elliptic hypergeometric integrals and series. We also propose s…
Bounded Littlewood identities
Eric M. Rains, S. Ole Warnaar
We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's parti…
Deformations of permutation representations of Coxeter groups
Eric M. Rains, Monica J. Vazirani
The permutation representation afforded by a Coxeter group W acting on the cosets of a standard parabolic subgroup inherits many nice properties from W such as a shellable Bruhat o…
Elliptic Littlewood identities
Eric M. Rains
We prove analogues for elliptic interpolation functions of Macdonald's version of the Littlewood identity for (skew) Macdonald polynomials, in the process developing an interpretat…
Correlation functions for random involutions
Peter J. Forrester, Taro Nagao, Eric M. Rains
Our interest is in the scaled joint distribution associated with -increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifyi…
BC_n-symmetric abelian functions
Eric M. Rains
We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing Koornwinder's orthogonal polynomials, and prove a number of their properties, most notably analo…