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Elliptic Littlewood identities

Authors
  • Rains, Eric M.
Type
Preprint
Publication Date
Feb 29, 2012
Submission Date
Jun 04, 2008
Identifiers
arXiv ID: 0806.0871
Source
arXiv
License
Yellow
External links

Abstract

We prove analogues for elliptic interpolation functions of Macdonald's version of the Littlewood identity for (skew) Macdonald polynomials, in the process developing an interpretation of general elliptic "hypergeometric" sums as skew interpolation functions. One such analogue has an interpretation as a "vanishing integral", generalizing a result of arXiv:math/0606204; the structure of this analogue gives sufficient insight to enable us to conjecture elliptic versions of most of the other vanishing integrals of arXiv:math/0606204 as well. We are thus led to formulate ten conjectures, each of which can be viewed as a multivariate quadratic transformation, and can be proved in a number of special cases.

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