Related papers: A generalization of Hall polynomials to ADE case

We investigate the problem whether a given multiplier of a tensor product of two algebras belongs to the tensor product of multiplier algebras. We give a characterization of such multipliers in the case when one of the algebras is the…

It is shown by the author in [J. Lie Theory 29:4, 1045-1070, 2019] that for every connected linear complex Lie group the algebra of polynomials (regular functions) is dense in the algebra of holomorphic functions of exponential type.…

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…

We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a…

We compute bifunctors cohomology for matrix polynomials under conjugation and detect candidates for universal classes in higher invariant theory.

We introduce a family of periods of mixed Tate motives called dissection polylogarithms, that are indexed by combinatorial objects called dissection diagrams. The motivic coproduct on the former is encoded by a combinatorial Hopf algebra…

We establish simple combinatorial descriptions of the radical and irreducible representations specifically for the descent algebra of a Coxeter group of type $D$ over any field.

We discuss a class of linear representations of the product poset of totally ordered sets $P= T_1 \times \cdots \times T_n$ which decompose into interval representations for block intervals. These can be characterised in terms of a…

Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda + \sum_{k = 1}^d [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are linear forms in…

We present the most general polynomial Lie algebra generated by a second order integral of motion and one of order M, construct the Casimir operator, and show how the Jacobi identity provides the existence of a realization in terms of…

We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a consequence, the characters of finite-dimensional…

We compute the characteristic polynomials of affine Cartan, adjacency matrices and Coxeter polynomials of the associated Coxeter system using Chebyshev polynomials. We give explicit factorization of these polynomials as products of…

We demonstrate how a simple linear-algebraic technique used earlier to compute low-degree cohomology of current Lie algebras, can be utilized to compute other kinds of structures on such Lie algebras, and discuss further generalizations,…

In [7, Papadima and Suciu, When does the associated graded Lie algebra of an arrangement group decompose? Comment. Math. Helv. {\bf 81:4} (2006), 859--875] it is proved that the holonomy Lie algebra of an arrangement of hyperplanes through…

We develop the notion of deformations using a valuation ring as ring of coefficients. This permits to consider in particular the classical Gerstenhaber deformations of associative or Lie algebras as infinitesimal deformations and to solve…

The goal of this paper is to supply an explicit description of the universal decomposition algebra of the generic polynomial of degree $n$ into the product of two monic polynomials, one of degree $r$, as a representation of Lie algebras of…

We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe…

We define the Hall algebra associated to any triangulated category under some finiteness conditions with the $t$-periodic translation functor $T$ for odd $t>1.$ This generalizes the results in \cite{Toen2005} and \cite{XX2006}.

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…

A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…