Related papers: Reduction of spherical functions
We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on…
Explicit generators are given for the ring of invariant polynomials under the coadjoint representation of certain inhomogeneous groups.
A presentation by generators and relations of the $n$th symmetric power $B$ of a commutative algebra $A$ over a field of characteristic zero or greater than $n$ is given. This is applied to get information on a minimal homogeneous…
Originally motivated by connections to integrable systems, two natural subalgebras of the rational Cherednik algebra have been considered in the literature. The first is the subalgebra of all degree zero elements and the second is the Dunkl…
We study the coadjoint representation of contractions of reductive Lie algebras associated with symmetric decompositions. Let $\frak g=\frak g_0\oplus \frak g_1$ be a symmetric decomposition of a reductive Lie algebra $\frak g$. Then the…
We investigate the representation theory of the rational and trigonometric Cherednik algebra of type $GL_n$ by means of combinatorics on periodic (or cylindrical) skew diagrams. We introduce and study standard tableaux and plane partitions…
We use derived Hall algebra of the category of nilpotent representations of Jordan quiver to reconstruct the theory of symmetric functions, focusing on Hall-Littlewood symmetric functions and various operators acting on them.
We define two subalgebras which can be seen as the quantization of the coordinate rings of the unipotent radical of the standard positive (respectively negative) Borel subgroup of $SL_{n+1}$. We give a presentation for these algebras and…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We extend results on finite dimensional nilpotent Lie algebras to Leibniz algebras and counterexamples to others are found. One generator algebras are used in these examples and are investigated further.
We give a minimal system of 476 generators (resp. 510 generators) for the algebra of SL(2,C)-covariant polynomials on binary forms of degree 9 (resp. degree 10). These results were only known as conjectures so far. The computations rely on…
We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are…
In [I. Arzhantsev and M. Zaidenberg, Borel subgroups of the automorphism groups of affine toric surfaces, arXiv:2507.09679 (2025)] we described the Borel subgroups and maximal solvable subgroups of the automorphism groups of affine toric…
The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra.…
This paper reexamines univariate reduction from a toric geometric point of view. We begin by constructing a binomial variant of the $u$-resultant and then retailor the generalized characteristic polynomial to fully exploit sparsity in the…
Harder's reduction theory provides filtrations of euclidean buildings that allow one to deduce cohomological and homological properties of S-arithmetic groups over global function fields. In this survey I will sketch the main points of…
The generators of the Jordanian quantum algebra ${\cal U}_h(sl(2))$ are expressed as nonlinear invertible functions of the classical $sl(2)$ generators. This permits immediate explicit construction of the finite dimensional irreducible…
Making use of a unified approach to certain classes of induced representations, we establish here a number of detailed spectral theoretic decomposition results. They apply to specific problems from non-commutative harmonic analysis, ergodic…
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra,…
We give a method of representing the modular invariant function by generators of a modular function field.