Bounded Littlewood Identities

Bounded Littlewood Identities PDF Author: Eric M. Rains
Publisher: American Mathematical Soc.
ISBN: 1470446901
Category : Education
Languages : en
Pages : 115

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Book Description
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.

Bounded Littlewood Identities

Bounded Littlewood Identities PDF Author: Eric M. Rains
Publisher: American Mathematical Soc.
ISBN: 1470446901
Category : Education
Languages : en
Pages : 115

Get Book Here

Book Description
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.

BOUNDED LITTLEWOOD IDENTITIES.

BOUNDED LITTLEWOOD IDENTITIES. PDF Author: ERIC M. RAINS
Publisher:
ISBN: 9781470465223
Category :
Languages : en
Pages :

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Abelian Networks IV. Dynamics of Nonhalting Networks

Abelian Networks IV. Dynamics of Nonhalting Networks PDF Author: Swee Hong Chan
Publisher: American Mathematical Society
ISBN: 1470451417
Category : Mathematics
Languages : en
Pages : 104

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On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function

On the Asymptotics to all Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function PDF Author: Athanassios S. Fokas
Publisher: American Mathematical Society
ISBN: 1470450984
Category : Mathematics
Languages : en
Pages : 114

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On the Symplectic Type of Isomorphisms of the $p$-Torsion of Elliptic Curves

On the Symplectic Type of Isomorphisms of the $p$-Torsion of Elliptic Curves PDF Author: Nuno Freitas
Publisher: American Mathematical Society
ISBN: 1470452103
Category : Mathematics
Languages : en
Pages : 105

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Isoperimetric Inequalities in Unbounded Convex Bodies

Isoperimetric Inequalities in Unbounded Convex Bodies PDF Author: Gian Paolo Leonardi
Publisher: American Mathematical Society
ISBN: 1470451182
Category : Mathematics
Languages : en
Pages : 86

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Intense Automorphisms of Finite Groups

Intense Automorphisms of Finite Groups PDF Author: Mima Stanojkovski
Publisher: American Mathematical Society
ISBN: 1470450038
Category : Mathematics
Languages : en
Pages : 117

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Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions

Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions PDF Author: Tom H. Koornwinder
Publisher: Cambridge University Press
ISBN: 1108916554
Category : Mathematics
Languages : en
Pages : 442

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Book Description
This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

Arthur Packets for $p$-adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples

Arthur Packets for $p$-adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples PDF Author: Clifton Cunningham
Publisher: American Mathematical Society
ISBN: 1470451174
Category : Mathematics
Languages : en
Pages : 232

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Brownian Regularity for the Airy Line Ensemble, and Multi-Polymer Watermelons in Brownian Last Passage Percolation

Brownian Regularity for the Airy Line Ensemble, and Multi-Polymer Watermelons in Brownian Last Passage Percolation PDF Author: Alan Hammond
Publisher: American Mathematical Society
ISBN: 1470452294
Category : Mathematics
Languages : en
Pages : 131

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