Related papers: Relative Serre duality for Hecke categories
We study a family of Siegel modular forms that are constructed using Jacobi forms that arise in Umbral moonshine. All but one of them arise as the Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie superalgebras.…
We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W . The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The…
We investigate a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms $F,G$ for orthogonal groups of signature $(2,n+2)$. In the case when $F$ is a Hecke eigenform and $G$ is a Maass lift of a Poincar\'e series, we…
The two most fundamental conjectures on the structure of the generic Hecke algebra $\mathcal{H}(W)$ associated with a complex reflection group $W$ state that $\mathcal{H}(W)$ is a free module of rank $|W|$ over its ring of definition, and…
The selfadjoint extensions of a closed linear relation $R$ from a Hilbert space ${\mathfrak H}_1$ to a Hilbert space ${\mathfrak H}_2$ are considered in the Hilbert space ${\mathfrak H}_1\oplus{\mathfrak H}_2$ that contains the graph of…
We obtain an irreducibility criterion for generalized principal series, extending known and frequently employed results for principal series. Our approach rests on a newly observed semi-direct product decomposition of the relative Weyl…
We compute Ext groups between Soergel Bimodules associated to the infinite/finite dihedral group for a realization in characteristic 0 and show that they are free right $R-$modules. In particular, we obtain an explicit diagrammatic basis…
We prove a new converse theorem for Borcherds' multiplicative theta lift which improves the previously known results. To this end we develop a newform theory for vector valued modular forms for the Weil representation, which might be of…
In this note, using tensor products with appropriate bimodules over Hecke algebras, we uniformly describe parabolic induction and Jacquet module. We also recover a result of Loke and Przebinda on construction of big theta lift in local…
A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category…
We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We…
Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors with supports in arbitrary subsets of Spec R, which is a natural generalization of right derived functors of section functors with supports in…
In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished embedded Hecke…
Using principal series Harish-Chandra modules, local cohomology with support in Schubert cells and twisting functors we construct certain modules parametrized by the Weyl group and a highest weight in the subcategory O of the category of…
Consider a pair of $S$-dual hyperspherical varieties $G\circlearrowright X$ and $G^\vee\circlearrowright X^\vee$ equipped with equivariant quantizations $Q(X)$, $Q(X^\vee)$. Assume that the local conjecture of Ben-Zvi, Sakellaridis and…
We establish a q-version of the Schur-Weyl duality, in which the role of the symmetric group is played by the Hecke algebra and the role of the enveloping algebra U(gl(N)) is played by the Reflection Equation algebra, associated with any…
First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…
We present the notion of "cyclic double multicategory", as a structure in which to organise multivariable adjunctions and mates. The classic example of a 2-variable adjunction is the hom/tensor/cotensor trio of functors; we generalise this…
Let $\mathcal C$ be a Krull-Schmidt triangulated category with shift functor $[1]$ and $\mathcal R$ be a rigid subcategory of $\mathcal C$. We are concerned with the mutation of two-term weak $\mathcal R[1]$-cluster tilting subcategories.…
We give another proof of the fact that there is a dual equivalence between the $\infty$-category of monoidal $\infty$-categories with left adjoint oplax monoidal functors and that with right adjoint lax monoidal functors by constructing a…