Related papers: Parabolic induction, categories of representations…
We study parabolic bundles on an algebraic curve in positive characteristic. Our motivation is to properly formulate Frobenius pull-backs of parabolic bundles in a way that extends various previous facts and arguments for the usual…
We give an analog of Frobenius' theorem about the factorization of the group determinant on the group algebra of finite abelian groups and we extend it into dihedral groups and generalized quaternion groups. Furthermore, we describe the…
This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…
We extend the notion of induced conjugacy classes in reductive groups, introduced by Lusztig and Spaltenstein for unipotent classes, to arbitrary classes. We study properties of equivariant fibrations of prehomogeneous affine spaces,…
We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation theory of rational Cherednik algebras. In…
In this paper, we introduce a new induction functor $\mathrm{Ind}^V_U$ between module categories corresponding to an embedding of vertex operator algebras (VOAs) $U \hookrightarrow V$. This induction functor is essentially defined at the…
The functor that takes a ring to its category of modules has an adjoint if one remembers the forgetful functor to abelian groups: the endomorphism ring of linear natural transformations. This uses the self-enrichment of the category of…
A pair of adjoint functors $(F,G)$ is called a Frobenius pair of the second type if $G$ is a left adjoint of $\beta F\alpha$ for some category equivalences $\alpha$ and $\beta$. Frobenius ring extensions of the second kind provide examples…
We show that induction along a Frobenius extension of Hopf algebras is a Frobenius monoidal functor in great generality, in particular, for all finite-dimensional and all pointed Hopf algebras. As an application, we show that induction…
We define proper, free and commuting partial actions on upper semicontinuous bundles of $C^*-$algebras. With such, we construct the $C^*-$algebra induced by a partial action and a partial actions on that algebra. Using those action we give…
We will present an algebra describing a mixed paraparticle model, known in the bibliography as "The Relative Parabose Set (\textsc{Rpbs})". Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom…
The tensor functor called $\alpha$-induction produces a new unitary fusion category from a Frobenius algebra, or a $Q$-system, in a braided unitary fusion category. A bi-unitary connection, which is a finite family of complex number subject…
An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…
We define a C*-hull for a *-algebra, given a notion of integrability for its representations on Hilbert modules. We establish a local-global principle which, in many cases, characterises integrable representations on Hilbert modules through…
A classical result of Sherman says that if the space of self-adjoint elements in a $C^*$-algebra $\mathcal{A}$ is a lattice with respect to its canonical order, then $\mathcal{A}$ is commutative. We give a new proof of this theorem which…
For a reductive group G defined over an algebraically closed field of positive characteristic, we show that the Frobenius contraction functor of G-modules is right adjoint to the Frobenius twist of the modules tensored with the Steinberg…
We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra ${\mathcal P}$ of an affine Lie algebra ${\mathfrak G}$, our main result establishes the…
We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e.…
We construct a model of type theory enjoying parametricity from an arbitrary one. A type in the new model is a semi-cubical type in the old one, illustrating the correspondence between parametricity and cubes. Our construction works not…
We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified…