Related papers: Quantum symmetric conjugacy classes of non-excepti…

Let $G$ be a simple complex classical group and $\g$ its Lie algebra. Let $\U_\hbar(\g)$ be the Drinfeld-Jimbo quantization of the universal enveloping algebra $\U(\g)$. We construct an explicit $\U_\hbar(\g)$-equivariant quantization of…

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…

In this short note, we classify pairs of conjugacy classes of the symmetric group such that any non-linear irreducible character of the symmetric group vanishes on at least one of them.

Classical symmetric pairs consist of a symmetrizable Kac-Moody algebra $\mathfrak{g}$, together with its subalgebra of fixed points under an involutive automorphism of the second kind. Quantum group analogs of this construction, known as…

To any complex Hadamard matrix we associate a quantum permutation group. The correspondence is not one-to-one, but the quantum group encapsulates a number of subtle properties of the matrix. We investigate various aspects of the…

We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…

A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters

Let G be a simple algebraic group over an algebraically closed field k. We classify the spherical conjugacy classes of G.

There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…

The role of quantum groups and braid groups in the description of Standard Model particles is discussed. Some recent results on the use of the quantum group $SU_q(3)$ as a flavour symmetry are reviewed and a connection between two…

In 1999 V. Ivanov and S. Kerov observed that structure constants of algebras of conjugacy classes of symmetric groups $S_n$ admit a stabilization (in a non-obvious sense) as $n\to \infty$. We extend their construction to a class of pairs of…

We prove a convolution formula for the conjugacy classes in symmetric groups conjectured by the second author. A combinatorial interpretation of coefficients is provided. As a main tool we introduce new semigroup of partial permutations. We…

The notion of quantum matrix pairs is defined. These are pairs of matrices with non-commuting entries, which have the same pattern of internal relations, q-commute with each other under matrix multiplication, and are such that products of…

Although the conjugacy classes of the general linear group are known, it is not obvious (from the canonic form of matrices) that two permutation matrices are similar if and only if they are conjugate as permutations in the symmetric group,…

We realize the quantum loop groups and shifted quantum loop groups of arbitrary types, possibly non symmetric, using critical K-theory. This generalizes the Nakajima construction of symmetric quantum loop groups via quiver varieties to non…

This is a survey of some recent progress on quantum symmetric pairs and applications. The topics include quasi K-matrices, $\imath$Schur duality, canonical bases, super Kazhdan-Lusztig theory, $\imath$Hall algebras, current presentations…

We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.

We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial…

Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…

Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…