Related papers: Birational Weyl group action arising from a nilpot…

We discuss a conjecture which says that the automorphism group of the Weyl algebra in characteristic zero is canonically isomorphic to the automorphism group of the corresponding Poisson algebra of classical polynomial symbols. Several…

We introduce braided Lie bialgebras as the infinitesimal version of braided groups. They are Lie algebras and Lie coalgebras with the coboundary of the Lie cobracket an infinitesimal braiding. We provide theorems of transmutation, Lie…

A Lie algebra L is known to be nilpotent if it admits a grading by (Zp, +) with support X not containing 0. It is also known that the class of L can be bounded by some explicit function of |X|. We generalise this and other classical results…

We find a general framework for the construction of birational involutions on two- and three-dimensional varieties obtained from $\mathbb P^2$, $\mathbb P^1\times \mathbb P^1$, and $\mathbb P^3$ by blow-up at nine, respectively eight…

We describe infinitesimally Dirac groupoids via geometric objects that we call Dirac bialgebroids. In the two well-understood special cases of Poisson and presymplectic groupoids, the Dirac bialgebroids are equivalent to the Lie…

We study the Segal-Bargmann transform on a motion group Rn n K; where K is a compact subgroup of SO(n): A characterization of the Poisson integrals associated to the Laplacian on Rn n K is given. We also establish a Paley-Wiener type…

We construct an analogue of Whittaker reduction for Poisson actions of a semisimple complex Poisson-Lie group G. The reduction takes place along a class of transversal slices to unipotent orbits in G, which are generalizations of the…

We give relations between dynamical Poisson groupoids, classical dynamical Yang--Baxter equations and Lie quasi-bialgebras. We show that there is a correspondance between the class of bidynamical Lie quasi-bialgebras and the class of…

Let $M$ be a $G$-covering of a nilpotent orbit in $\g$ where $G$ is a complex semisimple Lie group and $\g=\text{Lie}(G)$. We prove that under Poisson bracket the space $R[2]$ of homogeneous functions on $M$ of degree 2 is the unique…

In this paper, we obtain relations in the Weyl groups of Kac-Moody algebras that come from mutation classes of skew-symmetrizable matrices. These relations generalize those obtained by Barot and Marsh for finite type. As an application, we…

We define a multiple Dirichlet series whose group of functional equations is the Weyl group of the affine Kac-Moody root system $\tilde{A}_n$, generalizing the theory of multiple Dirichlet series for finite Weyl groups. The construction is…

We develop a structure theory for transposed Poisson algebras over fields of characteristic different from two. In particular, we prove that every finite-dimensional transposed Poisson algebra over an algebraically closed field decomposes…

We define noncommutative deformations $W_q^s(G)$ of algebras of functions on certain (finite coverings of) transversal slices to the set of conjugacy classes in an algebraic group $G$ which play the role of Slodowy slices in algebraic group…

Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the action of a simple Lie algebra g are…

We give a systematic study of the model theory of generic nilpotent groups and Lie algebras. We show that the Fra\"iss\'e limit of 2-nilpotent groups of exponent $p$ studied by Baudisch is 2-dependent and NSOP$_{1}$. We prove that the class…

Many interesting C*-algebras can be viewed as quantizations of Poisson manifolds. I propose that a Poisson manifold may be quantized by a twisted polarized convolution C*-algebra of a symplectic groupoid. Toward this end, I define…

We consider the conjugation-action of the Borel subgroup of the symplectic or the orthogonal group on the variety of nilpotent complex elements of nilpotency degree $2$ in its Lie algebra. We translate the setup to a…

It is well known that n x n upper-triangular real matrices with 1's on the diagonal form a nilpotent Lie group with an interesting family of non-isotropic dilations and corresponding geometry, as in [9]. Here we look at p-adic versions of…

We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on…

Let g be a complex simple Lie algebra and Uq(Lg) its quantum loop algebra, where q is not a root of unity. We give an explicit formula for the quantum Weyl group action of the coroot lattice Q of g on finite-dimensional representations of…