排序方式: 共有9条查询结果,搜索用时 31 毫秒
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We give new realizations of the crystal bases of the Verma modules and the irreducible highest weight modules over the quantum generalized Kac–Moody algebra U q (A ∞) and the quantum Monster algebra using Nakajima monomials. Moreover, another realization of the crystals B(∞) and B(λ) over U q (A ∞) using triangular matrices and tableaux are given. 相似文献
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Georgia Benkart Seok-Jin Kang Hyeonmi Lee Kailash C. Misra Dong-Uy Shin 《Compositio Mathematica》2001,126(1):91-111
We prove that the multiplicity of an arbitrary dominant weight for an irreducible highest weight representation of the affine Kac–Moody algebra A
(1)
r
is a polynomial in the rank r. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks. 相似文献
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Seok-Jin Kang Jeong-Ah Kim Hyeonmi Lee Dong-Uy Shin 《Transactions of the American Mathematical Society》2004,356(6):2349-2378
In this paper, we give a new realization of crystal bases for finite-dimensional irreducible modules over classical Lie algebras. The basis vectors are parameterized by certain Young walls lying between highest weight and lowest weight vectors.
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Dong-Uy Shin 《代数通讯》2013,41(1):129-142
In this article, we give a new realization of crystal bases for irreducible highest weight modules over U q (G 2) in terms of monomials. We also discuss the natural connection between the monomial realization and tableau realization. Communicated by K. Misra 相似文献
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In this paper, we give a new realization of the crystal basis B(∞) using modified Nakajima monomials for the quantum finite algebras. Moreover, as an application, we obtain the image of
the Kashiwara embedding Ψ
ι
from this realization of B(∞).
Presented by Alain Verschoren. 相似文献
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Zigzag strip bundles are new combinatorial models realizing the crystals B(∞) for the quantum affine algebras \(U_{q}(\mathfrak {g})\), where \(\mathfrak {g}=B_{n}^{(1)},D_{n}^{(1)}\), \(D_{n+1}^{(2)}\), \(C_{n}^{(1)}\), \(A_{2n-1}^{(2)}\), \(A_{2n}^{(2)}\). Recently, these models were used to the realization of highest weight crystals except for the highest weight crystal B(Λ0) over the quantum affine algebra \(U_{q}(C_{n}^{(1)})\). In this paper, we construct the highest weight crystal B(Λ0) over the quantum affine algebra \(U_{q}(C_{n}^{(1)})\) using zigzag strip bundles, which completes the realizations of all highest weight crystals over \(U_{q}(\mathfrak {g})\). 相似文献
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