Bounded Littlewood Identities (Memoirs of the American Mathematical Society) - Softcover

Eric M. Rains (author) & S. Ole Warnaar (author)

Softcover

ISBN 10: 1470446901 ISBN 13: 9781470446901

Publisher: American Mathematical Society, 2021

Synopsis

"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 partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon's famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n,R), O(n)as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers-Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulasfor Kaneko-Macdonald-type basic hypergeometric series"--

About this title

About the Author

Eric M. Rains, California Institute of Technology, Pasadena, CA

S. Ole Warnaar, The University of Queensland, Brisbane, Queensland, Australia

Edition details

• Publisher: American Mathematical Society
• Publication date: 2021
• Language: English
• ISBN 10: 1470446901
• ISBN 13: 9781470446901
• Binding: Paperback
• Number of pages: 115