Related papers: Spherical principal series of quantum Harish-Chand…
This paper extends the Bohr-Sommerfeld quantization of the spherical pendulum to a full quantum theory. This the first application of geometric quantization to a classical system with monodromy.
In this paper we study the category of Harish-Chandra bimodules $HC_{\chi,\psi}$ in the Deligne category $\text{Rep}(GL_t)$. In particular, we answer Question 3.25 posed in Pavel Etingof's paper arXiv:1407.0373 and determine for which…
We construct minimal Eisenstein integrals for a reductive symmetric space G/H as matrix coefficients of the minimal principal series of G. The Eisenstein integrals thus obtained include those from the \sigma-minimal principal series. In…
In this manuscript we make a general study of the representations realized, for a reductive Lie group of Harish-Chandra class, on the compactly supported sheaf cohomology groups of an irreducible finite-rank polarized homogeneous vector…
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems as well as disordered ones. Quasiperiodic criticality was previously understood only in the special limit where the…
We report on some recent work on deformation of spaces, notably deformation of spheres, describing two classes of examples. The first class of examples consists of noncommutative manifolds associated with the so called $\theta$-deformations…
We reconstruct finite-dimensional quantum theory from categorical principles. That is, we provide properties ensuring that a given physical theory described by a dagger compact category in which one may `discard' objects is equivalent to a…
Let $k(S^2_q)$ be the "coordinate ring" of a quantum sphere. We introduce the cotangent module on the quantum sphere as a one-sided $k(S^2_q)$-module and show that there is no Yang-Baxter type operator converting it into a…
We discuss some basic issues that arise when one attempts to model quantum mechanical systems on a computer, and we describe the mathematical structure of the resulting discretized cannonical commutation relations.
The notion of a Harish-Chandra bimodule, i.e. finitely generated $U(\mathfrak{g})$-bimodule with locally finite adjoint action, was generalized to any filtered algebra in a work of Losev [Ivan Losev, Dimensions of irreducible modules over…
In \cite{nr} Narasimhan and Ramanan and in \cite{desing}, Seshadri constructed desingularisations of the moduli space $M^{ss}_{_{\text{SL}(2)}}$ of semistable $\SL(2)$-bundles on a smooth projective curve $C$ of genus $g \geq 3$. Seshadri's…
Mathematical physicists have studied degenerations of Lie groups and their representations, which they call contractions. In this paper we study these contractions, and also other families, within the framework of algebraic families of…
Let $A=\mathbb{C}[t_1^{\pm1},t_2^{\pm1}]$ be the algebra of Laurent polynomials in two variables and $B$ be the set of skew derivations of $A$. Let $L$ be the universal central extension of the derived Lie subalgebra of the Lie algebra…
We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.
Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of constructing and studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of…
If $\Gamma$ is a subalgebra of $A$, then an $A$-module is called a Harish-Chandra module if it is the direct sum of its generalized weight spaces with respect to $\Gamma$. In 1994, Drozd, Futorny, and Ovsienko defined a generalization of a…
Employing ideas of noncommutative geometry, certain dimensional invariant for quantum homogeneous spaces has been proposed and here we take up its computation for quaternion spheres.
We study Harish-Chandra bimodules for the rational Cherednik algebra associated to the symmetric group $S_{n}$. In particular, we show that for any parameter $c \in \mathbb{C}$, the category of Harish-Chandra $H_{c}$-bimodules admits a…
Topological classifications of quantum critical systems have recently attracted growing interest, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, such classifications remain largely…