Hasil untuk "math.QA"

G. Lusztig

This represents a talk given at the International Conference for Basic Science, July 2025. We review the theory of canonical bases of quantum groups and its relation with the theory of total positivity.

Thomas Willwacher

We discuss the cohomology of the bridgeless graph complex, that is, the subcomplex of the Kontsevich graph complex spanned by bridgeless graphs.

Zhaobing Fan, Haitao Ma, Zhicheng Zhang

We establish a duality between a pair of mirabolic quantum groups, i.e., the mirabolic counterpart of quantum Howe duality.

Andrey Mudrov

We construct a $U_q(\mathrm{so}(2n+1))$-equivariant local star-product on the complex sphere $\mathbb{S}^{2n}$ as a Non-Levi conjugacy class $SO(2n+1)/SO(2n)$.

Frédéric Chapoton

One considers weighted sums over points of lattice polytopes, where the weight of a point v is the monomial q^f(v) for some linear form f. One proposes a q-analogue of the classical theory of Ehrhart series and Ehrhart polynomials, including Ehrhart reciprocity and involving evaluation at the q-integers.

Malihe Yousofzadeh

We give a complete description of Lie algebras graded by an infinite irreducible locally finite root system.

Tomasz Brzeziński, Zhengming Jiao

The theory of R-smash products for Hopf quasigroups is developed.

Nanhua Xi

The paper has been withdrawn.

Gabriella Böhm

This is a preprint version of a chapter for Handbook of Algebra.

Clark Alexander

We give an algorithm for computing matrix corepresentations for special linear and special unitary quantum groups using a combinatorial re-indexing of basis elements.

A. Kazarnovski-Krol

Integral of a certain multivalued form over cycle $\pmbΔ$ provides zonal spherical function of type $A_n$. This paper is devoted to quantum group analysis and verification of monodromy properties of the distinguished cycle $\pmbΔ$. Zonal spherical function is a particular conformal block of $WA_n$-algebra.

Dmitri Nikshych, Vladimir Turaev, Leonid Vainerman

We use categories of representations of finite dimensional quantum groupoids (weak Hopf algebras) to construct ribbon and modular categories that give rise to invariants of knots and 3-manifolds.

G. Felder, A. Varchenko

This is the talk of the second author at the meeting "Topological Methods in Physical Sciences", London, November 2000. We review our work on KZB equations.

Mico Durdevic

A noncommutative-geometric generalization of the classical concept of spinor structure is presented. This is done in the framework of the formalism of quantum principal bundles. In particular, analogs of the Dirac operator and the Laplacian are introduced and analyzed. A general construction of examples of quantum spaces with a spinor structure is presented.

Toshiyuki Abe

We prove that the vertex operator algebra $V_{Zα}^{+}$ is rational if $<α,α>/2$ is a prime integer.

Israel Gelfand, Vladimir Retakh

A version of the classical Vieta theorem for free noncommuting variables is given. It leads to a new start in a construction of noncommutative symmetric functions

Olga Nanasiova

In this paper we will study a function of simultaneus measurements for quantum events (s-map) which will be compared with the conditional states on an orthomodular lattice as a basic structure for quantum logic.

Ivan Cherednik, Yavor Markov

We use a degeneration of the 1D double affine Hecke algebra and the Dunkl operator to study systematically nonsymmetric Bessel functions and their truncations.

Reinhard Haering-Oldenburg

We define an action of Artin's braid group on a finite dimensional algebra.

W-S. Chung

In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with $q$ a root of unity.