Related papers: Generalization of modular lowering operators for G…
For an algebraically closed base field of characteristic p>0, a new algorithm to construct some non-zero GL(n-1)-high weight vectors of irreducible rational GL(n)-modules is suggested. It is based on successively applying Kleshchev's…
In this paper, we find an explicit combinatorial criterion for the existence of a nonzero GL_{n-1}(K)-high weight vector of weight (\lambda_1,...,\lambda_{i-1},\lambda_i-d,\lambda_{i+1},..., \lambda_{n-1}), where d<char K and K is an…
Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of regular functions on…
Let G be symmetrizable Kac-Moody Lie algebra. In this paper we describe a new class of central operators generalising the Casimir operator. We also prove some properties of these operators and show that these operators move highest weight…
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…
The ``$D$'' matrices for all states of the two fundamental representations and octet are shown in the generalized Euler angle parameterization. The raising and lowering operators are given in terms of linear combinations of the left…
We introduce a class of multidimensional Schr\"odinger operators with elliptic potential which generalize the classical Lam\'e operator to higher dimensions. One natural example is the Calogero--Moser operator, others are related to the…
In this paper, we define generalized Casimir operators for a loop contragredient Lie superalgebra and prove that they commute with the underlying Lie superalgebra. These operators have applications in the decomposition of tensor product…
Let $G={\rm GL}_n$ be the general linear group over an algebraically closed field $k$, let $\mathfrak g=\mathfrak gl_n$ be its Lie algebra and let $U$ be the subgroup of $G$ which consists of the upper uni-triangular matrices. Let…
In this article, we geometrically study the partial Bernstein-Zelevinsky operator introduced in the author's thesis, which generalizes the original Bernstein-Zelevinsky operator. We relate the partial Bernstein-Zelevinsky operator to the…
We apply recent knowledge and techniques of the new generalized upper and lower Legendre conjugates to the theory of weight functions in the sense of Braun-Meise-Taylor and study in detail the effects on the corresponding associated weight…
We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal…
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…
For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an…
We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order…
In the first part of the paper we defined and studied a binary operation on the set of irreducible components of Lusztig's nilpotent varieties of a quiver. For type $A$ we conjecture, following Geiss and Schr\"oer, that this operation is…
In this paper, we present a vertex operator approach to construct and compute all complex irreducible characters of the general linear group $\GL_n(\mathbb F_q)$. Green's theory of $\GL_n(\mathbb F_q)$ is recovered and enhanced under the…
We develop general expressions for the raising and lowering operators that belong to the orthogonal polynomials of hypergeometric type with discrete and continuous variable. We construct the creation and annihilation operators that…
Let G=GL_n be the general linear group over an algebraically closed field k and let g=gl_n be its Lie algebra. Let U be the subgroup of G which consists of the upper unitriangular matrices. Let k[g] be the algebra of polynomial functions on…
In this paper, we gave a weighted compactness theory for the generalized commutators of vecotor-valued multilinear Calder\'{o}n-Zygmund operators. This was done by establishing a weighted Fr\'{e}chet-Kolmogorov theorem, which holds for…