Related papers: Presentations of projective quantum groups
Given a quantum permutation group $G\subset S_N^+$, with orbits having the same size $K$, we construct a universal matrix model $\pi:C(G)\to M_K(C(X))$, having the property that the images of the standard coordinates $u_{ij}\in C(G)$ are…
We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.
We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a…
Easy quantum groups are compact matrix quantum groups, whose intertwiner spaces are given by the combinatorics of categories of partitions. This class contains the symmetric group and the orthogonal group as well as Wang's quantum…
We study the construction of premonoidal categories, where the pentagon relation fails, through representations of finite group algebras and their quantum doubles. Both finite group algebras and their quantum doubles have a finite number of…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
For the projective unitary group $PU_n$ with a maximal torus $T_{PU_n}$ and Weyl group $W$, we show that the integral restriction homomorphism \[\rho_{PU_n} \colon H^*(BPU_n;\mathbb{Z})\rightarrow H^*(BT_{PU_n};\mathbb{Z})^W\] to the…
In this paper, we construct certain unipotent representations for the real orthogonal group and the metaplectic group in the sense of Vogan. Our construction is based on quantum induction which involves the compositions of even number of…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
The main result of the paper is the characterization of those locally compact quantum groups with projection, i.e. non-commutative analogs of semidirect products, which are extensions as defined by L. Vainerman and S. Vaes. It turns out…
Though the irreducible representations of the Poincare' group form the groundwork for the formulation of relativistic quantum theories of a particle, robust classes of such representations are missed in current formulations of these…
In this paper we introduce a projective invarinat measure on the special unitary group. It is directly related to transition probabilities. It has some interesting connection with convex geometry. Applications to approximation of quantum…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
The orthogonal group acts on the space of several $n\times n$ matrices by simultaneous conjugation. For an infinite field of characteristic different from two, relations between generators for the algebra of invariants are described. As an…
Consider the pseidounitary group $G=U(p,q)$ and its compact subgroup $K=U(p)$. We construct an explicit unitary intertwining operator from the tensor product of a holomorphic representation and a antiholomorphic representation of $G$ to the…
In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…
This paper proves that the characteristic polynomial is a complete unitary invariant for pairs of projection matrices. Some special cases involving three or more projections are also considered.
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
Let $ G $ be a connected semisimple Lie group with finite center. We prove a formula for the inner product of two cuspidal automorphic forms on $ G $ that are given by Poincar\'e series of $ K $-finite matrix coefficients of an integrable…
We study the projective special Kaehler condition on groups, providing an intrinsic definition of homogeneous projective special Kaehler that includes the previously known examples. We give intrinsic defining equations that may be used…