Transfer Matrices of Rational Spin Chains via Novel BGG-Type Resolutions
Transfer Matrices of Rational Spin Chains via Novel BGG-Type Resolutions
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DOI：
10.1007/s00220-022-04620-6
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发表时间：
2021-12
影响因子：
2.4
通讯作者：
Rouven Frassek;I. Karpov;A. Tsymbaliuk
中科院分区：
文献类型：
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作者：
Rouven Frassek;I. Karpov;A. Tsymbaliuk
我们得到了经典李代数的不可约有限维表示的转移矩阵的BGG型公式，其最高权是基本权的倍数，并且可以提升到Yangian上的表示。这些转移矩阵表示为某些无限维最高权表示（如抛物Verma模及其推广）在辅助空间中的转移矩阵。我们进一步将相应的无穷维转移矩阵分解为两个QuerterQ算子的乘积，这两个算子来自我们以前的研究Frassek et al.（Adv. Math. 401：108283，2022），Frassek and Tsymbaliuk（Commun. 392：545-619，2022）。我们的方法是至关重要的是基于新的BGG型决议的有限维模，这自然产生的几何限制的Cousin复杂的相对局部上同调群的部分标志varietyG/Pstratified由轨道上的丰富的线丛。
We obtain BGG-type formulas for transfer matrices of irreducible finite-dimensional representations of the classical Lie algebras, whose highest weight is a multiple of a fundamental one and which can be lifted to the representations over the Yangian. These transfer matrices are expressed in terms of transfer matrices of certain infinite-dimensional highest weight representations (such as parabolic Verma modules and their generalizations) in the auxiliary space. We further factorise the corresponding infinite-dimensional transfer matrices into the products of two BaxterQ-operators, arising from our previous study Frassek et al. (Adv. Math. 401:108283, 2022), Frassek and Tsymbaliuk (Commun. Math. Phys. 392:545–619, 2022) of the degenerate Lax matrices. Our approach is crucially based on the new BGG-type resolutions of the finite-dimensional-modules, which naturally arise geometrically as the restricted duals of the Cousin complexes of relative local cohomology groups of ample line bundles on the partial flag varietyG/Pstratified by-orbits.