arXiv math/05034612005-03math.QA

Free product formulae for quantum permutation groups

Teodor Banica, Julien Bichon

备注：: 31 pages
发表信息：: J. Inst. Math. Jussieu 6 (2007), 381-414

英文摘要：

Associated to a finite graph $X$ is its quantum automorphism group $G(X)$. We prove a formula of type $G(X*Y)=G(X)*_wG(Y)$, where $*_w$ is a free wreath product. Then we discuss representation theory of free wreath products, with the conjectural formula $μ(G*_wH)=μ(G)\boxtimesμ(H)$, where $μ$ is the associated spectral measure. This is verified in two situations: one using free probability techniques, the other one using planar algebras.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

追踪量子置换群的轨道

Tracing the orbitals of the quantum permutation group

本文通过非交换平坦矩阵模型证明量子置换群具有自由轨道，并给出中间量子子群及量子置换群上四次单项式Haar态的显式公式。

2024-08-21math.QA

Fusion products of twisted modules in permutation orbifolds

Let $V$ be a vertex operator algebra, $k$ a positive integer and $σ$ a permutation automorphism of the vertex operator algebra $V^{\otimes k}$. In this paper, we determine the fusion product of any $V^{\otimes k}$-module with any $σ$-twisted $V^{\otimes k}$-module.

2021-08-05math.QA

置换轨形中扭曲模的融合积：II

Fusion Products of Twisted Modules in Permutation Orbifolds: II

本文针对 CFT 型简单有理 $C_2$-余有限顶点算子代数的张量积，确定了任意置换生成循环群作用下扭曲模的融合积。

2024-11-24math.QA

Universal Deformation Formulae, Symplectic Lie groups and Symmetric Spaces

We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of a class of solvable Lie groups. We also study compatible co-products by generalizing the notion of smash product in the context of Hopf algebras.

2003-08-20math.QAmath.SG

Free wreath product by the quantum permutation group

A free wreath product construction of a Hopf algebra (or of a Woronowicz algebra) by Wang's quantum permutation group is done. It provides new examples of quantum groups and is useful to describe the quantum automorphism group of the n-times disjoint union of a finite connected graph.

2001-07-04math.QAmath.RA

q-Wakimoto Modules and Integral Formulae of the Quantum Knizhnik-Zamolodchikov Equations

Matrix elements of intertwining operators between $q$-Wakimoto modules associated to the tensor product of representations of $U_q(\widehat{sl_2})$ with arbitrary spins are studied. It is shown that they coincide with the Tarasov-Varchenko's formulae of the solutions of the qKZ equations. The result generalizes that of the previous paper [Kuroki K., Nakayashiki A., SIGMA 4 (2008), 049, 13 pages, arXiv:0802.1776].

2009-03-07math.QA

更多相关论文收起更多论文

Universal Deformation Formulae for Three-Dimensional Solvable Lie groups

We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of every three-dimensional solvable Lie group. We also study compatible co-products by generalizing the notion of smash product in the context of Hopf algebras. We investigate in particular the dressing action of the `book' group on SU(2).

2003-08-20math.QAmath.SG

Quantum Schubert polynomials and quantum Schur functions

We introduce the quantum multi-Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations the quantum double Schubert polynomial coincides with some quantum multi-Schur function and prove a quantum analog of the Nagelsbach-Kostka and Jacobi-Trudi formulae for the quantum double Schubert polynomials in the case of Grassmannian permutations. We prove, also, an analog of the Billey-Jockusch-Stanley formula for quantum Schubert polynomials. Finally we formulate two conjectures about the structure of quantum double and q…

1997-01-20math.QAq-alg

Twisted modules for tensor product vertex operator superalgebras and permutation automorphisms of odd order

We construct and classify $(1 \; 2\; \cdots \; k)$-twisted $V^{\otimes k}$-modules for $k$ odd and for $V$ a vertex operator superalgebra. This extends previous results of the author, along with Dong and Mason, classifying all permutation-twisted modules for tensor product vertex operator algebras, to the setting of vertex operator superalgebras for odd order permutations. We show why this construction does not extend to the case of permutations of even order in the superalgebra case and how the construction and classification in the even order case is fundamentally different than that for the…

2013-10-07hep-thmath.QA

Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups

We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are 2d TQFTs whose fusion rules can be diagonalized. We show that, in this special basis, the 0-form symmetries always act as permutations while 1-form symmetries act by phases. This leads to an explicit description of the gauging of these symmetries. One application of our results is a generalization of the equivariant Verlinde formula to the case of general Lie groups. The generalized formula leads to many predictions for the geometry of Hitchin moduli spaces, which we explicitly check in several cases with low genus an…

2021-11-15hep-thmath-phmath.AG

Twisted sectors for tensor product vertex operator algebras associated to permutation groups

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V^{\otimes k}. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V^{\otimes k} are isomorphic to the categories of weak, weak admissible and ordinary V-modules, respectively. The main result is an explicit construction of the weak g-twisted V^{\otimes k}-modules from weak V-modules. For an arbitrary permutation automorphism g of V^{\otimes k} the category of weak admissible g-twisted mod…

1999-12-16hep-thmath.QA

Permutation-twisted modules for even order cycles acting on tensor product vertex operator superalgebras

We construct and classify $(1 \; 2 \; \cdots \; k)$-twisted $V^{\otimes k}$-modules for $k$ even and $V$ a vertex operator superalgebra. In particular, we show that the category of weak $(1 \; 2 \; \cdots \; k)$-twisted $V^{\otimes k}$-modules for $k$ even is isomorphic to the category of weak parity-twisted $V$-modules. This result shows that in the case of a cyclic permutation of even order, the construction and classification of permutation-twisted modules for tensor product vertex operator superalgebras is fundamentally different than in the case of a cyclic permutation of odd order, as pr…

2014-01-25hep-thmath.QA

Character Formulae for Ortho-symplectic Lie Superalgebras $\mathfrak{osp}(n|2)$

The character formula of any finite dimensional irreducible module $L_λ$ for Lie superalgebra $\mathfrak{osp}(n|2)$ is computed. As a by-product, the decomposition of tensor module $L_λ\otimes \mathbb{C}^{n|2}$, where $\mathbb{C}^{n|2}$ is the natural representation, is obtained.

2010-01-22math.QAmath.RT

Order structure on the algebra of permutations and of planar binary trees

In "Hopf algebra of the planar binary trees", Adv. Math. 139 (1998), no. 2, 293--309, we constructed by induction a graded associative product on the vector space generated by the planar binary trees (resp. the permutations). In the present paper we prove an explicit formula for this product in terms of a partial order on the set of planar binary trees (resp. the weak Bruhat order on the symmetric groups).

2001-02-08math.COmath.QA