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010 a| 2022007657;

020 a| 9781470446901q| (paperback);

020 z| 9781470465223q| (epub);

035 a| (WaSeSS)ssj0002593141;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA404.5b| .R335 2021;

082 00 a| 515/.552| 23/eng20220428;

084 a| 05E05a| 05E10a| 17B67a| 33D672| msc;

100 1 a| Rains, Eric M.=| ^A631359;

245 10 a| Bounded littlewood identitiesh| [electronic resource] /c| Eric M. Rains, S. Ole Warnaar.;

260 a| Providence :b| American Mathematical Society,c| [2021];

300 a| vii, 115 pages :b| illustrations ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Volume 270, Number 1317 (first of 7 numbers);

504 a| Includes bibliographical references.;

506 a| Available only to authorized users.;

520 a| "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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Orthogonal polynomials.=| ^A58718;

650 0 a| Combinatorial identities.=| ^A123016;

650 7 a| Combinatorics -- Algebraic combinatorics -- Symmetric functions and generalizations.2| msc;

650 7 a| Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of representation theory.2| msc;

650 7 a| Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras.2| msc;

650 7 a| Special functions -- Basic hypergeometric functions -- Basic hypergeometric functions associated with root systems.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Warnaar, S. Ole.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6661108;

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

Author/creator	Rains, Eric M.
Other author	Warnaar, S. Ole.
Format	Electronic
Publication Info	Providence : American Mathematical Society, [2021]
Description	vii, 115 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Orthogonal polynomials. Combinatorial identities.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Volume 270, Number 1317 (first of 7 numbers)
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022007657
ISBN	9781470446901 (paperback)
ISBN	(epub)

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