Related papers: Markov semi-groups associated with the complex uni…

It was noticed recently that, given a metric space $(X,d_X)$, the equivalence classes of metrics on the disjoint union of the two copies of $X$ coinciding with $d_X$ on each copy form an inverse semigroup $M(X)$ with respect to…

We prove a geometrically meaningful stochastic representation of the derivative of the heat semigroup on sub-Riemannian manifolds with tranverse symmetries. This representation is obtained from the study of Bochner-Weitzenbock type formulas…

A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the…

In this article we calculate two aspects of the representation theory of a Brauer configuration algebra: its Cartan matrix, and the module length of its associated indecomposable projective modules. Then we introduce the concept of…

In this paper, we construct a representation of loop group and derive the formula of the corresponding representation of the affine Kac-Moody algebra with level 1. And we also provide a concrete realization of Whittaker functionals in the…

We classify the finite dimensional representations of the quantum symmetric pair coideal subalgebra $B_{\mathbf c}$ of type $DII$ corresponding to the symmetric pair $(so(2N),so(2N-1))$. For $B_{\mathbf c}$ defined over an arbitrary field…

We give negative answers to certain questions on abelian semisimple tensor categories raised by Bruno Kahn and Charles A. Weibel in connection with the preprint of Kahn "On the multiplicities of a motive" (arXiv:math/0610446), now published…

In this paper we consider weakly holomorphic modular forms (i.e. those meromorphic modular forms for which poles only possibly occur at the cusps) of weight $2-k\in 2\Z$ for the full modular group $\SL_2(\Z)$. The space has a distinguished…

We determine a substantial part of the unitary representation theory of the Drinfeld double of a $q$-deformation of a compact Lie group in terms of the complexification of the compact Lie group. Using this, we show that the dual of every…

In this paper, we systematically study generalized Markov numbers arising from semigroups of reduced integer matrices. This construction allows us to find these numbers by counting perfect matchings of a new family of bipartite graphs,…

We prove Feynman-Kac formulas for the semigroups generated by selfadjoint operators in a class containing Fr\"ohlich Hamiltonians known from solid state physics. The latter model multi-polarons, i.e., a fixed number of quantum mechanical…

We compute the exact thermal partition functions of a massive scalar field on flat spacetime backgrounds of the form $\mathbb R^{d-q}\times \mathbb T^{q+1}$ and show that they possess an ${\rm SL}(q+1,\mathbb Z)$ symmetry. Non-trivial…

For a maximal separable subfield $K$ of a central simple algebra $A$, we provide a semiring isomorphism between $K$-$K$-bimodules $A$ and $H$-$H$ bisets of $G = \Gal(L/F)$, where $F = \operatorname{Z}(A)$, $L$ is the Galois closure of…

In this paper, we study the fine Selmer groups of two congruent Galois representations over an admissible $p$-adic Lie extension. We show that under appropriate congruence conditions, if the dual fine Selmer group of one is pseudo-null, so…

We classify the finite-dimensional irreducible representations of the super Yangian associated with the orthosymplectic Lie superalgebra ${\frak osp}_{2|2n}$. The classification is given in terms of the highest weights and Drinfeld…

Beilinson--Bernstein localisation relates representations of a Lie algebra $\mathfrak{g}$ to certain $\mathcal{D}$-modules on the flag variety of $\mathfrak{g}$. In [arXiv:2002.01540], examples of $\mathfrak{sl}_2$-representations which…

Let $S$ be a semitopological semigroup and $\mathcal{CB}(S)$ denotes the $C^*$-algebra of all bounded complex valued continuous functions on $S$ with uniform norm. A function $f\in \mathcal{CB}(S)$ is left multiplicative \linebreak…

In a previous work, we have associated a complete differential graded Lie algebra to any finite simplicial complex in a functorial way. Similarly, we have also a realization functor from the category of complete differential graded Lie…

This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the $L^p$ norms of the…

We define a notion of modular forms of half-integral weight on the quaternionic exceptional groups. We prove that they have a well-behaved notion of Fourier coefficients, which are complex numbers defined up to multiplication by $\pm 1$. We…