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Bounded Littlewood identities / Eric M. Rains, S. Ole Warnaar.

Math/Physics/Astronomy Library QA3 .A57 no.1317
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LIBRA QA3 .A57 no.1-no.154, no.156-no.228, no.230-no.236, no.238-no.289, no.291-no.312, no.314-no.334, no.336-no.338
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Math/Physics/Astronomy Library QA3 .A57 no.313 (1984),no.335 (1985),no.339 (1986)-no.599 (1997) no.605 (1997)-no.860 (2006),no.865 (2006)-no.1243 (2019),no.1252 (2019)-no.1286 (2020),no.1288 (2020)-no.1385 (2022),no.1392 (2023)-no.1548 (2025),no.1554 (2025)-no.1620 (2026)
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Format:
Book
Author/Creator:
Rains, Eric M., author.
Warnaar, S. Ole, author.
Series:
Memoirs of the American Mathematical Society ; 0065-9266 no. 1317.
Memoirs of the American Mathematical Society, 0065-9266 ; number 1317
Language:
English
Subjects (All):
Polynomials.
Hypergeometric series.
Schur functions.
Partitions (Mathematics).
Physical Description:
vii, 115 pages : illustrations ; 26 cm.
Place of Publication:
Providence, RI : American Mathematical Society, [2021]
Summary:
"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 formulas for Kaneko-Macdonald-type basic hypergeometric series." -- page 5.
Contents:
Introduction: Littlewood identities ; Outline
Macdonald-Koornwinder theory
Virtual Koornwinder integrals
Bounded Littlewood identities
Applications
Open problems
Appendix A. The Weyl-Kac formula
Appendix B. Limits of elliptic hypergeometric integrals.
Notes:
"March 2021, volume 270, number 1317 (first of 7 numbers)."
Includes bibliographical references.
Other Format:
Online version:
ISBN:
9781470446901
1470446901
OCLC:
1261766847

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