Related papers: Integral objects and Deligne's category Rep(S_t)

Let $\mathcal {C}$ be a small category and let $R$ be a representation of the category $\mathcal {C}$, that is, a pseudofunctor from a small category to the category of small preadditive categories. In this paper, we mainly study the…

We introduce the notions of categorical integrals and categorical cointegrals of a finite tensor category $\mathcal{C}$ by using a certain adjunction between $\mathcal{C}$ and its Drinfeld center $\mathcal{Z}(\mathcal{C})$. These notions…

We introduce the notion of meromorphic tensor category and illustrate it in several examples. They include representations of quantum affine algebras, chiral algebras of Beilinson and Drinfeld, G-vertex algebras of Borcherds, and…

We study the covariance properties of the equations satisfied by the generating functions of the chiral operators R and T of supersymmetric SO(N)/Sp(N) theories with symmetric/antisymmetric tensors. It turns out that T is an affine…

We obtain a family of matrix integrals which decompose to a product of Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but generally speaking essentially differ from it). We obtain Plancherel formula for Berezin…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be…

We study abelian envelopes for pseudo-tensor categories with the property that every object in the envelope is a quotient of an object in the pseudo-tensor category. We establish an intrinsic criterion on pseudo-tensor categories for the…

We define the affine VW supercategory $\mathit{s}\hspace{-0.7mm}\bigvee\mkern-15mu\bigvee$, which arises from studying the action of the periplectic Lie superalgebra $\mathfrak{p}(n)$ on the tensor product $M\otimes V^{\otimes a}$ of an…

Let $H_{\mathbf{k}}$ be a symplectic reflection algebra corresponding to a cyclic subgroup $\Gamma \subseteq SL_2 \C$ of order $n$ and $U_{\mathbf{k}} = eH_{\mathbf{k}} e$ the spherical subalgebra of $H_{\mathbf{k}}$. We show that for…

We review some important facts about the structure of tensor products of finite dimensional representations of quantum affine algebras. This is done from the elementary standpoint of the representation theory of semisimple Lie algebras in…

For a rigid tensor abelian category $T$ over a field $k$ we introduce a notion of a normal quotient $q:T\to Q$. In case $T$ is a Tannaka category, our notion is equivalent to Milne's notion of a normal quotient. More precisely, if $T$ is…

Let $U'_q(\mathfrak{g})$ be a twisted affine quantum group of type $A_{N}^{(2)}$ or $D_{N}^{(2)}$ and let $\mathfrak{g}_{0}$ be the finite-dimensional simple Lie algebra of type $A_{N}$ or $D_{N}$. For a Dynkin quiver of type…

We introduce a symmetric monoidal category of modules over the direct limit queer superalgebra $\q (\infty)$. The category can be defined in two equivalent ways with the aid of the large annihilator condition. Tensor products of copies of…

We give a complete list of indecomposable exact module categories over the finite tensor category $\mathrm{Rep}(u_q(\mathfrak{sl}_2))$ of representations of the small quantum group $u_q(\mathfrak{sl}_2)$, where $q$ is a root of unity of odd…

In this paper, we study tensor (or monoidal) categories of finite rank over an algebraically closed field $\mathbb F$. Given a tensor category $\mathcal{C}$, we have two structure invariants of $\mathcal{C}$: the Green ring (or the…

This is the first in a series of papers in which we study representations of the Brauer category and its allies. We define a general notion of triangular category that abstracts key properties of the triangular decomposition of a semisimple…

In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…

We show the existence of a semisimple replete subcategory of Khovanov's Heisenberg category that retains the isomorphism data of objects for the full category. This leads to a noncommutative tensor-triangular geometric example of a monoidal…

We prove a version of the Deligne conjecture for $n$-fold monoidal abelian categories $A$ over a field $k$ of characteristic 0, assuming some compatibility and non-degeneracy conditions for $A$. The output of our construction is a weak…