Related papers: Simple biset functors and double Burnside rings

We construct an exact tensor functor from the category $\mathcal{A}$ of finite-dimensional graded modules over the quiver Hecke algebra of type $A_\infty$ to the category $\mathscr C_{B^{(1)}_n}$ of finite-dimensional integrable modules…

In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…

We study several structure aspects of functor categories from a small additive category to a module category, in particular the category F(A,K) of functors from finitely generated free modules over a commutative ring A to vector spaces over…

In this article, we introduce an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group $\mathbb{H}^n$. We completely characterize exponents $\alpha, \beta$ and $\gamma$ such that the operator is bounded…

Let $k$ be an algebraically closed field of characteristic $p>0$, let $R$ be a commutative ring, and let $\mathbb{F}$ be an algebraically closed field of characteristic 0. We consider the $R$-linear category $\mathcal{F}^\Delta_{Rpp_k}$ of…

Let G be a finite group and let p be a prime. A module for G over a field of characteristic p is called algebraic if it satisfies a polynomial, with addition and multiplication given by direct sum and tensor product. In some sense, having…

Let $G$ be a simply connected simple algebraic group over an algebraically closed field $k$ of characteristic $p>0$. The category of rational $G$-modules is not semisimple. We consider the question of when the tensor product of two simple…

This paper extends the notion of $B$-group to a relative context. For a finite group $K$ and a field $\mathbb{F}$ of characteristic 0, the lattice of ideals of the Green biset functor $\mathbb{F}B_K$ obtained by shifting the Burnside…

In this paper, we combine the concepts of the fibered Burnside ring and the character ring, viewing them as fibered biset functors, into what we call the global representation fibered ring of a finite group. We compute all ring…

We introduce the new notion of general bilinear forms (generalizing sesquilinear forms) and prove that for every ring $R$ (not necessarily commutative, possibly without involution) and every right $R$-module $M$ which is a generator (i.e.…

Given a finite group $G$, its double Burnside ring $B(G,G)$, has a natural duality operation that arises from considering opposite $(G,G)$-bisets. In this article, we systematically study the subgroup of units of $B(G,G)$, where elements…

This is the author's second paper treating the double coset problem for classical groups. Let $G$ be an algebraic group over an algebraically closed field $K$. The double coset problem consists of classifying the pairs $H,J$ of closed…

Let $G$ be the group of rational points of a split connected reductive group over a nonarchimedean local field of residue characteristic $p$. Let $I$ be a pro-$p$ Iwahori subgroup of $G$ and let $R$ be a commutative quasi-Frobenius ring. If…

In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of…

In this paper, we provide a solution to the open problem of computing the Fourier transform of a binary function defined over $n$-bit vectors taking $m$-bit vector values. In particular, we introduce the two-modular Fourier transform (TMFT)…

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over the field $K$, and let $I\subset S$ be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded $S$-modules $\Tor_i^S(M,I^k)$ and $\Ext^i_S(M,I^k)$ are…

We prove that the only separable commutative ring-objects in the stable module category of a finite cyclic p-group G are the ones corresponding to subgroups of G. We also describe the tensor-closure of the Kelly radical of the module…

Let G=GL(N), K=GL(p)xGL(q), where p+q=N, and n be a positive integer. We construct a functor from the category of Harish-Chandra modules for the pair (G,K) to the category of representations of the degenerate affine Hecke algebra of type…

We determine the composition factors of the $A$-fibered Burnside functor $kB^A$ for $p$-groups over a field $k$ of characteristic $q$ with $q\neq p$ and cyclic fiber group $A$. We also show that, in this case, $kB^A$ is uniserial.

Let $D\subseteq B$ be an extension of integral domains and $E$ a subset of the quotient field of $D$. We introduce the ring of \textit{$D$-valued $B$-rational functions on $E$}, denoted by $Int^R_B(E,D)$, which naturally extends the…