Related papers: Generalized blob algebras and alcove geometry
In this paper we give a streamlined overview of some of the recent constructions provided with K.-H. Neeb, G. \'Olafsson and collaborators for a new geometric approach to Algebraic Quantum Field Theory (AQFT). Motivations, fundamental…
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to…
We initiate the representation theory of the degenerate affine periplectic Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated representations when $n=2$. We show that any such representation that is…
This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a consequence we obtain a geometric and combinatorial description…
The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role. This result is essential for the theory of intertwiners…
We review some facts about the representation theory of the Hecke algebra. We adapt for the Hecke algebra case the approach of Okounkov and Vershik which was developed for the representation theory of symmetric groups. We justify an…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…
We further develop the abstract representation theory of affine Hecke algebras with arbitrary positive parameters. We establish analogues of several results that are known for reductive p-adic groups. These include: the relation between…
This paper gives an algebraic presentation of an algebra called the fused permutations algebra in the one-boundary case. It is obtained through a detailed study of the degenerate cyclotomic Hecke algebra. In particular, we prove that the…
The model of generalized quons is described in a purely algebraic way. Commutation relations and corresponding consistency conditions for our generalized quons system are studied in terms of quantum Weyl algebras. Fock space representation…
We explore the modular representation theory of affine and cyclotomic Yokonuma-Hecke algebras. We provide an equivalence between the category of finite dimensional representations of the affine (resp. cyclotomic) Yokonuma-Hecke algebra and…
This paper has two main purposes. Firstly we generalise Ram's explicit construction of calibrated representations of the affine Hecke algebra to the multi-parameter case (including the non-reduced $BC_n$ case). We then derive the Plancherel…
We introduce the concept of a covering of a graded pointed Hopf algebra. The theory developed shows that coverings of a bosonized Nichols algebra can be concretely expressed by biproducts using a quotient of the universal coalgebra covering…
It is well-known that affine Hecke algebras are very useful to describe the smooth representations of any connected reductive p-adic group G, in terms of the supercuspidal representations of its Levi subgroups. The goal of this paper is to…
We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type A. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we…
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
We give a geometric realization of the whole universal enveloping algebra of the Borcherds-Bozec algebra using quiver with loops via the motivic semi-derived Hall algebra approach. In particular, using acyclic quivers, we give a geometric…
We study the representation theory of a generalized graded Hecke algebra associated to a complex reflection group of type G(r,1,n), defined by Ram and Shepler. We use a realization of this algebra in the corresponding symplectic reflection…
Affine Hecke algebras arise naturally in the study of smooth representations of reductive $p$-adic groups. Finite dimensional complex representations of affine Hecke algebras (under some restriction on the isogeny class and the parameter…
For the coordinate algebras of connected affine algebraic groups, we explore the problem of finding a presentation by generators and relations canonically determined by the group structure.