Spaces of coinvariants and fusion product. I: From equivalence theorem to Kostka polynomials

DOI10.1215/S0012-7094-04-12533-3zbMath1129.17304arXivmath/0205324OpenAlexW1991823974MaRDI QIDQ1766401

Boris L. Feigin, Michio Jimbo, Tetsuji Miwa, Rinat Kedem, Sergey Loktev

Publication date: 7 March 2005

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0205324

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Applications of Lie (super)algebras to physics, etc. (17B81) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items

Two-dimensional current algebras and affine fusion product, Spaces of coinvariants and fusion product. II: \(\widehat{\mathfrak{sl}_2}\) character formulas in terms of Kostka polynomials, Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas, Demazure crystals and the Schur positivity of Catalan functions, The PBW filtration, Schubert varieties and the fusion products, Fermionic characters and arbitrary highest-weight integrable \({\widehat{\mathfrak{sl}}}_{r+1}\)-modules

Cites Work

• The Bethe Ansatz and the combinatorics of Young tableaux
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• Construction of modular branching functions from Bethe's equations in the 3-state Potts chain
• Supernomial coefficients, polynomial identities and \(q\)-series
• Berenstein-Zelevinsky triangles, elementary couplings, and fusion rules
• A compactification of configuration spaces
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• A bijection between Littlewood-Richardson tableaux and rigged configurations
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• Functional models of the representations of current algebras and semi-infinite Schubert cells
• Fermionic sum representations for conformal field theory characters
• Combinatorics of the \(\widehat{\mathfrak {sl}}_2\) spaces of coinvariants
• A generalization of the Kostka-Foulkes polynomials
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