Related papers: A classification of even representations onto 3-ad…

We study and classify almost all quantum SL(3,C)'s whose representation theory is ``similar'' to that of the (ordinary) group SL(3,C). Only one case, related to smooth elliptic curves, could not be treated completely.

Recently one of the authors obtained a classification of simple infinite-dimensional Lie superalgebras of vector fields which extends the well-known classification of E. Cartan in the Lie algebra case. The list consists of many series…

We propose a general algorithm to compute all the symmetry classes of any $\mathrm{SO}(3)$ or $\mathrm{O}(3)$ linear representation. This method relies on the introduction of a binary operator between sets of conjugacy classes of closed…

We continue the study of irreducible representations of the exceptional Lie superalgebra E(3,6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sl(3)\times sl(2)\times gl(1) as…

Let $k$ be an algebraically closed field of positive characteristic $p$. In this article, we classify representations of $\mathbb{G}_a \rtimes \mathbb{G}_m$ into ${\rm SL}(3, k)$, and thereby we classify fundamental representations of…

We classify rank one 2-representations of SL2, GL2 and SO3 web categories. The classification is inspired by similar results about quantum groups, given by reducing the problem to the classification of bilinear and trilinear forms, and is…

We obtain the equivariant K-homology of the classifying space \underline{E}SL(3,Z) from the computation of its Bredon homology with respect to finite subgroups and coefficients in the representation ring. We also obtain the corresponding…

In this article, we study the modular representations of the special linear group of degree two over a finite field in defining characteristic. In particular, we study the automorphisms of derived category of representations. We have been…

A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic representation theory of sl(2, C). This, combined with…

Let $\rho$ be a two-dimensional even Galois representation which is induced from a character $\chi$ of odd order of the absolute Galois group of a real quadratic field. After imposing some additional conditions on $\chi$, we attach $\rho$…

We introduce the notions of symmetric and symmetrizable representations of $\text{SL}_2(\mathbb{Z})$. The linear representations of $\text{SL}_2(\mathbb{Z})$ arising from modular tensor categories are symmetric and have congruence kernel.…

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…

We classify SL(2;C)-representations of a Brieskorn homology 3-sphere. We show any irreducible representation into SL(2;C) is conjugate to that into either SU(2) or SL(2;R). We also give a construction of SL(2;R)-representations for a…

A brief proof of Lie's classification of solvable algebras of vector fields on the plane is given. The proof uses basic representation theory and PDEs.

The general structure of the representation theory of a $Z_2$-graded coalgebra is discussed. The result contains the structure of Fourier analysis on compact supergroups and quantisations thereof as a special case. The general linear…

We compute the characters of real irreducible representations of SL(2,q), the special linear group on q letters, for an odd prime $q$. Moreover, we give the dimensions of these irreducible representations under the actions of cyclic…

We describe our conjecture about the irreducible unitary representations of reductive Lie groups, in the special case of $\mathrm{SL}(2,\mathbb{R})$.

The paper extends existing Lie algebra representation theory related to Lie algebra gradings. The notion of a representation compatible with a given grading is defined and applied to finite-dimensional representations of $sl(n,\mathbb{C})$…

For all odd primes N up to 500000, we compute the action of the Hecke operator T_2 on the space S_2(Gamma_0(N), Q) and determine whether or not the reduction mod 2 (with respect to a suitable basis) has 0 and/or 1 as eigenvalues. We then…

We construct an irreducible representation for the extended affine algebra of type $sl_2$ with coordinates in a quantum torus. We explicitly give formulas using vertex operators similar to those found in the theory of the infinite rank…