Equivariant factorization homology of global quotient orbifolds

Weelinck, T.A.N.

doi:10.1016/j.aim.2020.107072

Cited by 4 publications

(3 citation statements)

References 54 publications

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“…Hence it is natural to associate invariants to such orbifold surfaces constructed from a Z 2 D 2 -algebra via a formula like Equation (1.12.1). In the follow-up paper [Wee2] we make this idea precise by introducing Γ-equivariant factorization homology, where Γ can be an arbitrary finite group.…”

Section: The Reflection Equations Revisitedmentioning

confidence: 99%

A topological origin of quantum symmetric pairs

Weelinck

2019

Sel. Math. New Ser.

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It is well known that braided monoidal categories are the categorical algebras of the little two-dimensional disks operad. We introduce involutive little disks operads, which are Z 2 -orbifold versions of the little disks operads. We classify their categorical algebras and describe these explicitly in terms of a finite list of functors, natural isomorphisms and coherence equations. In dimension two, the categorical algebras are braided monoidal categories with an anti-involution together with a pointed module category carrying a universal solution to the (twisted) reflection equation. Main examples are obtained from the categories of representations of a ribbon Hopf algebra with an involution and a quasi-triangular coideal subalgebra, such as a quantum group and a quantum symmetric pair coideal subalgebra. Remark 1.10. The reflection equation algebra O q (G) is an (equivariant) quantization of the Semenov-Tian-Shansky Poisson bracket on O(G) [Mud06]. This algebra goes by many names: Majid's braided dual of U q (g) [Maj95], the quantum-loop algebra [AS96] and is isomorphic to the locally finite part of U q (g) via the Rosso form [KS09, Proposition 2.8].6

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Section: The Reflection Equations Revisitedmentioning

confidence: 99%

A topological origin of quantum symmetric pairs

Weelinck

2019

Sel. Math. New Ser.

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“…The type of factorisation homology we compute in this article is a special case of equivariant factorisation homology for global quotient orbifolds [Wee20]; namely the case of free actions. The general case, which requires additional input data, should give rise to field theories defined as functors out of the bordism category introduced in [GS21].…”

Section: Introductionmentioning

confidence: 99%

Finite symmetries of quantum character stacks

Keller¹,

Müller²

2021

Preprint

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For a finite group D, we study categorical factorisation homology on oriented surfaces equipped with principal D-bundles, which 'integrates' a (linear) balanced braided category A with D-action over those surfaces. For surfaces with at least one boundary component, we identify the value of factorisation homology with the category of modules over an explicit algebra in A, extending the work of Ben-Zvi, Brochier and Jordan to surfaces with D-bundles. Furthermore, we show that the value of factorisation homology on annuli, boundary conditions, and point defects can be described in terms of equivariant representation theory.Our main example comes from an action of Dynkin diagram automorphisms on representation categories of quantum groups. We show that in this case factorisation homology gives rise to a quantisation of the moduli space of flat twisted bundles.

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“…First we summarize the notion of equivariant factorization homology from [Wee18]: Let M be an ndimensional manifold equipped with the action of a finite group G and ρ :…”

Section: Introductionmentioning

confidence: 99%