Related papers: Bivariant $K$-theory and the Weyl algebra

We analyze the W_N^l algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l^{th} flow of the sl(N) KdV hierarchy. The W_4^3…

We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version…

We consider a connected compact Lie group K acting on a symplectic manifold M such that a moment map m exists. A pull-back function via m Poisson commutes with all K-invariants. Guillemin-Sternberg raised the problem to find a converse. In…

We consider the Iwahori-Hecke algebra associated to an almost split Kac-Moody group $G$ (affine or not) over a nonarchimedean local field $K$. It has a canonical double-coset basis $(T_{\mathbf w})_{\mathbf w\in W^+}$ indexed by a…

We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple…

The first (associative) Weyl algebra is formally rigid in the classical sense. In this paper, we show that it can however be formally deformed in a nontrivial way when considered as a so-called hom-associative algebra, and that this…

For any Hecke symmetry $R$ there is a natural quantization $A_n(R)$ of the Weyl algebra $A_n$. The aim of this paper is to study some general ring-theoretic aspects of $A_n(R)$ and its relations to formal deformations of $A_n$. We also…

First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field.…

Motivated by Weyl algebra analogues of the Jacobian conjecture and the Tame Generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl algebras. In particular, our results cover the Weyl-Hayashi…

Let $\mathcal{G}$ be an algebraic quantum group. We introduce an equivariant algebraic $kk$-theory for $\mathcal{G}$-module algebras. We study an adjointness theorem related with smash product and trivial action. We also discuss a duality…

We compute Hochschild homology and cohomology of a class of generalized Weyl algebras (for short GWA, defined by Bavula in St.Petersbourg Math. Journal 1999 4(1) pp. 71-90). Examples of such algebras are the n-th Weyl algebras, U(sl_2),…

For any two involutions y,w in a Weyl group (y\le w), let P_{y,w} be the polynomial defined in [KL]. In this paper we define a new polynomial P^\sigma_{y,w} whose i-th coefficient is a_i-b_i where the i-th coefficient of P_{y,w} is a_i+b_i…

Let R be the set of isomorphism classes of ideals in the Weyl algebra $A=A_{1}$, and let C be the set of isomorphism classes of triples (V; X, Y), where V is a finite-dimensional (complex) vector space, and X, Y are endomorphisms of V such…

The inversion formula is given for automorphisms of the Weyl algebras with polynomial coefficients over a field of characteristic zero. The theorem of Gabber on the degree of polynomial automorphism is extended. It is proved that any…

This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…

We prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation…

By means of the notions of cross product algebras of the theory of quantum groups, in the context of classical Hopf algebra structures, we deduce some known structures of Weyl algebras type (as the Drinfeld quantum double, the restricted…

Let $\mathfrak g$ be a simple Lie algebra. There are classical formulas for the Jacobians of the generating invariants of the Weyl group of $\mathfrak g$ and of the images under the Harich-Chandra projection of the generators of…

In this article we apply the duality technique of R. Howe to study the structure of the Weyl algebra. We introduce a one-parameter family of ``ordering maps'', where by an ordering map we understand a vector space isomorphism of the…

Lie-theoretic structures of type $E_8$ (e.g., Lie groups and algebras, Hecke algebras and Kazhdan-Lusztig cells, ...) are considered to serve as a `gold standard' when it comes to judging the effectiveness of a general algorithm for solving…