Related papers: Representations of Quantum Groups defined over Com…
We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…
We categorify the idempotented form of quantum sl(n).
This chapter appears in "Fractional Quantum Hall Effects: New Development," edited by B. I. Halperin and J. K. Jain (World Scientific, 2020). The chapter begins with a primer on composite fermions, and then reviews three directions that…
The goal of this paper is threefold. First, we describe the notion of dissociation for closed subgroups of the group of permutations on a countably infinite set and explain its numerous consequences on unitary representations…
We juxtapose two approaches to the representations of the super-Heisenberg group. Physical one, sometimes called concrete approach, based on the super-wave functions depending on the anti-commuting variables, yielding the harmonic…
These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.
We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic…
We study Cox rings of crepant resolutions of quotient singularities $\mathbb{C}^3/G$ where $G$ is a finite subgroup of $SL(3,\mathbb{C})$. We use them to obtain information on the geometric structure of these resolutions, number of…
Answering a question of Shuzhou Wang we give a description of quantum $\SO(3)$ groups of Podle\'s as universal objects. We use this result to give a complete classification of all continuous compact quantum group actions on $M_2$.
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
Semi-direct products of finite groups have permutation representations that are constructed from the permutation representations of their constituents. One can envision these in a metaphoric sense in which a rope is made from a bundle of…
Notes of a 8h course given at the University of G\"oteborg during an Erasmus exchange visit, June 11-15, 2018. It is intended for PhD and graduate students familiar with $C^*$-algebras but not specializing in quantum groups. The proofs, if…
We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…
The new approach to the theory of complex representrations of the finite symmetric groups which based on the notions of Coxeter generators., Gelfand-Zetlin algebras, Hecke algebra, Young-Jucys-Murphi generators and which hardly used…
We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…
Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The…
We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is…
We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.
In this paper, we prove that for any odd prime larger than 3, the modular group representation associated to the SO$(p)_2$-TQFT can be defined over the ring of integers of a cyclotomic field. We will provide explicit integral bases. In the…
Given a subgroup H of a finite group G, we begin a systematic study of the partial representations of G that restrict to global representations of H. After adapting several results from [DEP00] (which correspond to the case where H is…