Related papers: Correction to "Harmonic representatives for cuspid…
The proof of the coincidence of the Gysin morphism in motivic cohomology and the usual pushout on Chow groups has been improved (see Lemma 3.3 and Proposition 3.11)
We establish the vanishing for non-trivial unitary representations of the bounded cohomology of SL_d up to the rank. It holds more generally for uniformly bounded representations on superreflexive spaces. The same results are obtained for…
These are lecture notes (by the first author) from a course (by the second author) given over two extended semesters at the University of Sydney. The first part provides an introduction to the Langlands correspondence from an arithmetical…
A corrigendum of a former result on semisimplicity of the category of integrable modules of a q-boson algebra is given with a counter example.
In this PhD thesis we will discuss some aspects in Commutative Algebra which have interactions with Algebraic Geometry, Representation Theory and Combinatorics. In particular, in the first chapter we will focus on understanding when certain…
This paper is based on the author's paper "Koszul duality in deformation quantization, I", with some improvements. In particular, an Introduction is added, and the convergence of the spectral sequence in Lemma 2.1 is rigorously proven. Some…
We continue the~study of embeddings between different classes of Sobolev spaces of differential forms started in 2006 in a~paper by Gol$'$dshtein and Troyanov. As in this paper, our study is based on relations between $L_{q,p}$-cohomology…
Homotopy coherence has a considerable history, albeit also by other names. For this volume highlighting symmetries, the appropriate use is: Homotopy coherence of representations, at one time known as strong homotopy representations. We…
We establish combinatorial and inductive formulas for Kazhdan-Lusztig polynomials associated to covexillary elements in classical types, extending results of Boe, Lascoux-Sch\"{u}tzenberger, Sankaran-Vanchinathan, and Zelevinsky for…
The article is devoted to a comparison of the \v{C}ech cohomology with the coefficients in a presheaf of Abelian groups and the topos cohomology of the sheaf generated by this presheaf for a poset with the Aleksandrov topology. The article…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of representations of the conformal algebra induced from the maximal cuspidal parabolic.
The goal of this paper is to prove how Arthur's results, in the case of split odd orthogonal p-adic groups, imply the Langlands' classification of discrete series. Of course this need the validity of ''fundamental'' lemmas which are not yet…
Building upon the work of Pavel in [P. Kolesnikov, Journal of Mathematical Physics, 56, 7 (2015)], we first present the cohomology of averaging operators on the Lie conformal algebras and use it to develop the cohomology of averaging Lie…
Let $G$ be a connected complex simple Lie group, and let $\widehat{G}^{\mathrm{d}}$ be the set of all equivalence classes of irreducible unitary representations with non-vanishing Dirac cohomology. We show that $\widehat{G}^{\mathrm{d}}$…
We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded…
We study a notion of cusp forms for the symmetric spaces G/H with G = SL(n,R) and H = S(GL(n-1,R) x GL(1,R)). We classify all minimal parabolic subgroups of G for which the associated cuspidal integrals are convergent and discuss the…
Kazhdan and Lusztig identified the affine Hecke algebra $\mathcal{H}$ with an equivariant $K$-group of the Steinberg variety, and applied this to prove the Deligne-Langlands conjecture, i.e., the local Langlands parametrization of…
Partial representations of Hopf algebras were motivated by the theory of partial representations of groups. Alves, Batista e Vercruysse introduced partial representations of a Hopf algebra and showed that, as in the case of partial groups…
We study properties of compactly supported $p$-adic pro-\'etale cohomology of smooth partially proper rigid analytic varieties. In particular, we prove a comparison theorem, in a stable range, with compactly supported syntomic cohomology,…
The purpose of this paper is to study the properties of holomorphic Poisson manifolds $(M,\pi)$ under the assumption of $\partial_{}\bar{\partial}$--lemma or $\partial_{\pi}\bar{\partial}$--lemma. Under these assumptions,we show that the…