Lusztig's \(q\)-analogue of weight multiplicity and one-dimensional sums for affine root systems
From MaRDI portal
Publication:854109
DOI10.1016/j.aim.2006.03.001zbMath1111.22014arXivmath/0508511OpenAlexW2025848202MaRDI QIDQ854109
Cédric Lecouvey, Mark Shimozono
Publication date: 7 December 2006
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0508511
Symmetric functions and generalizations (05E05) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representation theory for linear algebraic groups (20G05) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)
Related Items
On \(q\)-analogs of weight multiplicities for the Lie superalgebras \(\mathfrak{gl}(n,m)\) and \(\mathfrak{spo}(2n,M)\) ⋮ Quantization of branching coefficients for classical Lie groups ⋮ Hall-Littlewood polynomials, alcove walks, and fillings of Young diagrams ⋮ Stable rigged configurations for quantum affine algebras of nonexceptional types ⋮ Affine crystals, one-dimensional sums and parabolic Lusztig \(q\)-analogues ⋮ From Macdonald polynomials to a charge statistic beyond type \(A\) ⋮ Atomic decomposition of characters and crystals ⋮ Weight Multiplicities and Young Tableaux Through Affine Crystals
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A plactic algebra for semisimple Lie algebras
- Branching rules, Kostka-Foulkes polynomials and \(q\)-multiplicities in tensor product for the root systems \(B_n\), \(C_n\) and \(D_n\)
- Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank
- Kostka polynomials and energy functions in solvable lattice models
- Perfect crystals of quantum affine Lie algebras
- Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
- Schensted-type correspondence, plactic monoid, and jeu de taquin for type \(C_n\)
- Combinatorial \(R\) matrices for a family of crystals: \(B_n^{(1)}\), \(D_n^{(1)}\), \(A_{2n}^{(2)}\) and \(D_{n+1}^{(2)}\) cases
- Schensted-type correspondences and plactic monoids for types \(B_n\) and \(D_n\)
- \(X=M\) for symmetric powers
- Deformed universal characters for classical and affine algebras
- A duality between \(q\)-multiplicities in tensor products and \(q\)-multiplicities of weights for the root systems \(B\), \(C\) or \(D\)
- Products and Plethysms of Characters with Orthogonal, Symplectic and Symmetric Groups
- Characters and the q -Analog of Weight Multiplicity
- AFFINE CRYSTALS AND VERTEX MODELS
- Virtual crystals and fermionic formulas of type 𝐷_{𝑛+1}⁽²⁾, 𝐴_{2𝑛}⁽²⁾, and 𝐶_{𝑛}⁽¹⁾
