Related papers: Generalized Burnside-Grothendieck ring functor and…

In this note, we compute the split Grothendieck ring of a generalized category of Soergel bimodules of type $A_2$, where we take one generator for each reflection. We give a presentation by generators and relations of it and a…

Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…

For each integer $t$ a tensor category $V_t$ is constructed, such that exact tensor functors $V_t \longrightarrow C$ classify dualizable $t$-dimensional objects in $C$ not annihilated by any Schur functor. This means that $V_t$ is the…

We study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

We prove that the algebra of functions on the cotangent bundle $T^*(G/U_P)$ of the parabolic base affine space for a reductive group $G$ and a parabolic subgroup $P$ is isomorphic to the subalgebra of the functions on $G \times L \times…

We show that taking the set of primitive idempotents of commutative association schemes is a functor from the category of commutative association schemes with surjective morphisms to the category of finite sets with surjective partial…

Let $G$ and $\tilde G$ be reductive groups over a local field $F$. Let $\eta : \tilde G \to G$ be a $F$-homomorphism with commutative kernel and commutative cokernel. We investigate the pullbacks of irreducible admissible…

We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups $\operatorname{GL}_n$, the two-parameter…

By conformal welding, there is a pair of univalent functions $(f,g)$ associated to every point of the complex K\"ahler manifold $\Mob(S^1)\bk\Diff_+(S^1)$. For every integer $n\geq 1$, we generalize the definition of Faber polynomials to…

Let $\widetilde{G}$ be a split connected reductive group with connected center $Z$ over a local non-Archimedean field $F$ of residue characteristic $p$, let $\widetilde{K}$ be a hyperspecial maximal compact open subgroup in $\widetilde{G}$.…

Suppose that $G$ is a simple adjoint reductive group over $\mathbf{Q}$, with an exceptional Dynkin type, and with $G(\mathbf{R})$ quaternionic (in the sense of Gross-Wallach). Then there is a notion of modular forms for $G$, anchored on the…

Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same…

The double Burnside $R$-algebra $\text{B}_R(G,G)$ of a finite group $G$ with coefficients in a commutative ring $R$ has been introduced by S. Bouc. It is $R$-linearly generated by finite $(G,G)$-bisets, modulo a relation identifying…

Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this…

The goal of this paper is to introduce the notion of $G$-Frobenius manifolds for any finite group $G$. This work is motivated by the fact that any $G$-Frobenius algebra yields an ordinary Frobenius algebra by taking its $G$-invariants. We…

Consider the Mackey functor assigning to each finite group G the Green ring of finitely generated kG-modules, where k is a field of characteristic p>0. Thevenaz foresaw in 1988 that the class of primordial groups for this functor is the…

Let $U_\varepsilon^{\mathrm{res}}(L\mathfrak{sl}_2)$ be the restricted integral form of the quantum loop algebra $U_q(L\mathfrak{sl}_2)$ specialised at a root of unity $\varepsilon$. We prove that the Grothendieck ring of a tensor…

Let $\mathfrak{Var}_k^G$ denote the category of pairs $(X,\sigma)$, where $X$ is a variety over $k$ and $\sigma$ is a group action on $X$. We define the Grothendieck ring for varieties with group actions as the free abelian group of…

We study cocommutative Hopf dialgebras through generalized digroups and rack combinatorics. We prove that the rack functor obtained from the adjoint rack bialgebra factorizes through the digroup of group-like elements. More precisely, for…

Deligne's category $\underline{{\rm Rep}}(S_t)$ is a tensor category depending on a parameter $t$ "interpolating" the categories of representations of the symmetric groups $S_n$. We construct a family of categories $\mathcal{C}_\lambda$…