相关论文: Recursion relations and branching rules for simple…
It is demonstrated that decompositions of integrable highest weight modules of a simple Lie algebra with respect to its reductive subalgebra obey the set of algebraic relations leading to the recursive properties for the corresponding…
For any representation of a complex simple Lie algebra $\mathfrak{sl}_n$, one problem of branching rules to $\mathfrak{sl}_2$-subalgebra is to determine the multiplicity of each irreducible component. In this paper, we derive a recursion…
In this paper we prove that every recursively presented Lie algebra over a field which is a finite extention of its simple subfield can be embedded in a recursively presented Lie algebra defined by relations which are equalities of…
Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching rules. We demonstrate that splint properties implementation drastically…
We develop an algebraic approach to the branching of representations of the general linear Lie superalgebra $\mathfrak{gl}_{p|q}({\mathbb C})$, by constructing certain super commutative algebras whose structure encodes the branching rules.…
Splint of root system of simple Lie algebra appears naturally in the study of (regular) embeddings of reductive subalgebras. It can be used to derive branching rules. Application of splint properties drastically simplifies calculations of…
A root system is splint if it is a decomposition into a union of two root systems. Examples of such root systems arise naturally in studying embeddings of reductive Lie subalgebras into simple Lie algebras. Given a splint root system, one…
Splints of root system of simple lie algebras appears naturally on studies of embedding of reductive subalgebras. A splint can be used to construct a branching rules as implementation of this idea simplifies calculation of branching…
We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…
From the matrix point of view, we use the recursion to discuss four combinatorial numbers in terms of the integer lattice paths, this is different from Andr\'a's method (Andra). We give four tables and matrices, and their relations, and…
We introduce a new partial order on the set of all antichains of a fixed size in any poset. When applied to minuscule posets, these partial orders give rise to distributive lattices that appear in the branching rules for minuscule…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
In this paper, first we introduce the notion of quadratic Rota-Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie bialgebras and quadratic Rota-Baxter Lie algebras of nonzero…
Splint is a decomposition of root system into union of root systems. Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching…
We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields ($\leq…
We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…
We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…
This paper provides a short introduction to scalar, bosonic, and fermionic superfield component expansion based on the branching rules of irreducible representations in one Lie algebra (in our case, $\mathfrak{su}(32)$, and also…
Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…
This article examines matrices whose entries are determined by recursive relations of the form $A_{i, j} = x A_{i, j-1} + y A_{i-1, j-1} + z A_{i-1, j}$, where $x, y, z$ are constants, and the initial conditions are defined along the first…