Three Combinatorial Models for $$ _ $$ Crystals, with Applications to Cylindric Plane Partitions
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Publication:5503912
DOI10.1093/imrn/rnm143zbMath1233.17019arXivmath/0702062OpenAlexW1570030269MaRDI QIDQ5503912
Publication date: 21 January 2009
Published in: International Mathematics Research Notices (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0702062
Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)
Related Items (17)
Heisenberg algebra, wedges and crystals ⋮ Some useful theorems for asymptotic formulas and their applications to skew plane partitions and cylindric partitions ⋮ Modular Nekrasov-Okounkov formulas ⋮ Duality and bicrystals on infinite binary matrices ⋮ ROUQUIER’S CONJECTURE AND DIAGRAMMATIC ALGEBRA ⋮ The 𝐴₂ Andrews–Gordon identities and cylindric partitions ⋮ Rogers-Ramanujan identities and the Robinson-Schensted-Knuth correspondence ⋮ Kirillov-Reshetikhin crystals \(B^{1, s}\) for \(\widehat{\mathfrak{s}\mathfrak{l}}_n\) using Nakajima monomials ⋮ Cyclic sieving phenomenon on dominant maximal weights ⋮ Skew doubled shifted plane partitions: calculus and asymptotics ⋮ Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type \(A\) ⋮ Triple crystal action in Fock spaces ⋮ Realization of Kirillov-Reshetikhin crystals \(B^{1,s}\) for \(\widehat{\mathfrak{sl}}_n\) using Nakajima monomials ⋮ Cyclic sieving phenomenon on dominant maximal weights over affine Kac-Moody algebras ⋮ Yangians and cohomology rings of Laumon spaces ⋮ Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via \(K\)-theory of affine Laumon spaces ⋮ The \(A_2\) Rogers-Ramanujan identities revisited
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