Level one perfect crystals for \(B_n^{(1)}\), \(C_n^{(1)}\), and \(D_n^{(1)}\)
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Publication:1305083
DOI10.1006/jabr.1998.7806zbMath0941.17010OpenAlexW2019061652MaRDI QIDQ1305083
Publication date: 3 August 2000
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jabr.1998.7806
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)
Related Items (10)
Level 0 Monomial Crystals ⋮ Kirillov-Reshetikhin crystals for nonexceptional types ⋮ Construction of perfect crystals conjecturally corresponding to Kirillov-Reshetikhin modules over twisted quantum affine algebras ⋮ Demazure structure inside Kirillov-Reshetikhin crystals ⋮ Combinatorial structure of Kirillov-Reshetikhin crystals of type \(D_n^{(1)}\), \(B_n^{(1)}\), \(A^{(2)}_{2n-1}\) ⋮ Perfect crystals for \(U_q(D_4^{(3)})\) ⋮ A bijection between type \(D_n^{(1)}\) crystals and rigged configurations ⋮ Finite-dimensional crystals \(B^{2,s}\) for quantum affine algebras of type \(D^{(1)}_{n}\) ⋮ Existence of Kirillov–Reshetikhin crystals for nonexceptional types ⋮ Virtual crystals and fermionic formulas of type 𝐷_{𝑛+1}⁽²⁾, 𝐴_{2𝑛}⁽²⁾, and 𝐶_{𝑛}⁽¹⁾
Cites Work
- Quantum R matrices related to the spin representations of \(B_ n\) and \(D_ n\)
- On crystal bases of the \(q\)-analogue of universal enveloping algebras
- Perfect crystals of quantum affine Lie algebras
- Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras
- Crystals for Demazure modules of classical affine Lie algebras
- Perfect crystals of \(U_q(G_2^{(1)})\)
- Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
- Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras
- Crystalizing the q-analogue of universal enveloping algebras
- AFFINE CRYSTALS AND VERTEX MODELS
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