arXiv subjects

Mao Hoshino

Publications and source records attributed to Mao Hoshino.

5 recordsLinked to original sources

arXiv2025

Semisimple module categories with fusion rules of the compact full flag manifold type

We classify semisimple left module categories over the representation category of a type A quantum group whose fusion rules arise from the maximal torus. The classification is connected to equivariant Poisson structures on compact full flag manifolds in the operator-algebraic setting, and on semisimple coadjoint orbits in the algebraic setting. We also provide an explicit construction based on the BGG categories of deformed quantum enveloping algebras, whose unitarizability corresponds to being of quotient type. Finally, we present a brief discussion of the non-quantum case.

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arXiv2025

Finite index quantum subgroups of discrete quantum groups

We show that finite index quantum subgroups of a discrete quantum group are induced from finite index quantum subgroups of the unimodularization. As an application, we classify all finite index quantum subgroups of free products of the duals of connected simply-connected compact Lie groups. We also put proofs for some fundamental facts on finite index right coideals of compact quantum groups.

math.OA↗

arXiv2024

Polynomial families of quantum semisimple coadjoint orbits via deformed quantum enveloping algebras

We construct a polynomial family of semisimple left module categories over the representation category of the Drinfeld-Jimbo deformation, with the fusion rule of the representation category of each Levi subalgebra. In this construction we perform a kind of generalized parabolic induction using a deformed quantum enveloping algebra, whose definition depends on an arbitrary choice of a positive system and corresponds to De Commer's definition for the standard positive system. These algebras define a sheaf of algebras on the toric variety associated to the root system, which contains the moduli of equivariant Poisson brackets. This fact finally produces the family of 2-cocycle. We also obtain a comparison theorem between our module categories and module categories induced from our construction for intermediate Levi subalgebras. The construction of deformed quantum enveloping algebras and the comparison theorem are discussed in the integral setting of Lusztig's sense.

math.QA↗

arXiv2024

A note on quantum subgroups of free quantum groups

In this short note, quantum subgroups in finite free products of the Pontryagin duals of free unitary quantum groups are classified. They correspond to pairs of a subgroup $Γ$ and a subset $S$ of the free group $\mathbb{F}_n$ such that $S$ is $Γ$-invariant, containing $Γ$, and connected in the Cayley graph of $\mathbb{F}_n$

math.OA↗

arXiv2023

Equivariant covering spaces of quantum homogeneous spaces

We develop a fundamental theory of compact quantum group equivariant finite extensions of C*-algebras. In particular we focus on the case of quantum homogeneous spaces and give a Tannaka-Krein type result for equivariant correspondences. As its application, we show that every Jones' value appears as the index of an equivariant conditional expectation. In the latter half of this paper, we give an imprimitivity theorem in some cases: for general compact quantum groups under a finiteness conditions, and for the Drinfeld-Jimbo deformation $G_q$ of a simply-connected compact Lie group $G$. As an application, we give a complete classification of finite index discrete quantum subgroups of $\widehat{G_q}$.

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