Related papers: A Cousin Complex for the Quantum Projective Space

A global representation is a compatible collection of representations of the outer automorphism groups of the groups belonging to some collection of finite groups $\mathscr{U}$. Global representations assemble into an abelian category…

Motivated by recent advances in the categorification of quantum groups at prime roots of unity, we develop a theory of 2-representations for 2-categories enriched with a p-differential which satisfy finiteness conditions analogous to those…

We provide a systematic treatment of boundaries based on subgroups $K\subseteq G$ with the Kitaev quantum double $D(G)$ model in the bulk. The boundary sites are representations of a $*$-subalgebra $\Xi\subseteq D(G)$ and we explicate its…

Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n-1 quantum groups for q a root of unity. Representations which have the maximal dimension and…

This article develops a practical technique for studying representations of $\Bbbk$-linear categories arising in the categorification of quantum groups. We work in terms of locally unital algebras which are $\mathbb{Z}$-graded with graded…

We study projective unitary (co)representations of compact quantum groups and the associated second cohomology theory. We introduce left/right/bi/strongly projective corepresentations and study them in details. In particular, we prove that…

Quantum toroidal algebras (or double affine quantum algebras) are defined from quantum affine Kac-Moody algebras by using the Drinfeld quantum affinization process. They are quantum groups analogs of elliptic Cherednik algebras (elliptic…

Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations…

We show that the pair given by the power set and by the "Grassmannian"(set of all subgroups) of an arbitrary group behaves very much like the pair given by a projective space and its dual projective space. More precisely, we generalize…

We give a complete construction of the Bernstein-Gelfand-Gelfand complex on real or complex projective space using minimal ingredients.

We construct a special principal series representation for the modular double $U_{q\tilde{q}}(g_R)$ of type $A_r$ representing the generators by positive essentially self-adjoint operators satisfying the transcendental relations that also…

We prove various finiteness and representability results for cohomology of finite flat abelian group schemes. In particular, we show that if $f\colon X\rightarrow \mathrm{Spec}(k)$ is a projective scheme over a field $k$ and $G$ is a finite…

In this paper we present an abstract framework for construction of Banach spaces of distributions from group representations. This generalizes the theory of coorbit spaces initiated by H.G. Feichtinger and K. Gr\"ochenig in the 1980's.…

Let $G$ be an adjoint quasi-simple group defined and split over a non-archimedean local field $K$. We prove that the dual of the Steinberg representation of $G$ is isomorphic to a certain space of harmonic cochains on the Bruhat-Tits…

Francois Rodier proved that it is possible to view smooth representations of certain totally disconnected abelian groups (the underlying additive group of a finite-dimensional p-adic vector space, for example) as sheaves on the Pontryagin…

We build representations of the affine and double affine braid groups and Hecke algebras of type $C^\vee C_n$, based upon the theory of quantum symmetric pairs $(U,B)$. In the case $U=U_q(gl_N)$, our constructions provide a quantization of…

Following the recent approach of using order domains to construct Grobner bases from general projective varieties, we examine the parity and time-reversal arguments relating de Witt and Lyman's assertion that all path weights associated…

Like quantum groups, quantum groupoids frequently appear in pairs of mutually dual objects. We develop a general Pontrjagin duality theory for quantum groupoids in the algebraic setting that extends Van Daele's duality theory for multiplier…

There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…

The classical duality theory associates to an abelian group a dual companion. Passing to a non-abelian group, a dual object can still be defined, but it is no longer a group. The search for a broader category which should include both the…