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We define a ribbon category , depending on a parameter β, which encompasses Cautis, Kamnitzer and Morrison's spider category, and describes for the monoidal category of representations of generated by exterior powers of the vector representation and their duals. We identify this category with a direct limit of quotients of a dual idempotented quantum group , proving a mixed version of skew Howe duality in which exterior powers and their duals appear at the same time. We show that the category gives a unified natural setting for defining the colored link invariant (for ) and the colored HOMFLY-PT polynomial (for β generic). 相似文献
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Masoumah Al-Ali 《Journal of Pure and Applied Algebra》2019,223(12):5430-5443
Let be a simple, finite-dimensional complex Lie algebra, and let denote the universal affine vertex algebra associated to at level k. The Cartan involution on lifts to an involution on , and we denote by the orbifold, or fixed-point subalgebra, under this involution. Our main result is an explicit minimal strong finite generating set for for generic values of k. 相似文献
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Luigi Ambrosio Shouhei Honda Jacobus W. Portegies David Tewodrose 《Journal of Functional Analysis》2021,280(10):108968
In this paper we study the family of embeddings of a compact space into via eigenmaps. Extending part of the classical results [10], [11] known for closed Riemannian manifolds, we prove convergence as of the rescaled pull-back metrics in induced by . Moreover we discuss the behavior of with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative -convergence in the noncollapsed setting for all , a result new even for closed Riemannian manifolds and Alexandrov spaces. 相似文献
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《Discrete Mathematics》2022,345(11):113058
Given an undirected graph , a conflict-free coloring with respect to open neighborhoods (CFON coloring) is a vertex coloring such that every vertex has a uniquely colored vertex in its open neighborhood. The minimum number of colors required for such a coloring is the CFON chromatic number of G, denoted by .In previous work [WG 2020], we showed the upper bound , where denotes the distance to cluster parameter of G. In this paper, we obtain the improved upper bound of . We also exhibit a family of graphs for which , thereby demonstrating that our upper bound is tight. 相似文献
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Julia Semikina 《Journal of Pure and Applied Algebra》2019,223(10):4509-4523
I. Hambleton, L. Taylor and B. Williams conjectured a general formula in the spirit of H. Lenstra for the decomposition of for any finite group G and noetherian ring R. The conjectured decomposition was shown to hold for some large classes of finite groups. D. Webb and D. Yao discovered that the conjecture failed for the symmetric group , but remarked that it still might be reasonable to expect the HTW-decomposition for solvable groups. In this paper we show that the solvable group is also a counterexample to the conjectured HTW-decomposition. Nevertheless, we prove that for any finite group G the rank of does not exceed the rank of the expression in the HTW-decomposition. We also show that the HTW-decomposition predicts correct torsion for for any finite group G. Furthermore, we prove that for any degree other than the conjecture gives a correct prediction for the rank of . 相似文献
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