Related papers: Concrete Fock representations of Mickelsson-Faddee…
To some braiding R of Hecke type (a Hecke symmetry) we put into correspondence an associative algebra called the modified Reflection Equation Algebra (mREA). We construct a series of matrices L_(m), m=1,2,... with entries belonging to mREA…
Dosi and, quite recently, the author showed that, on the character space of a nilpotent Lie algebra, there exists a sheaf of Fr\'echet--Arens--Michael algebras (of noncommutative holomorphic functions in the complex case and of…
A universality of deformed Heisenberg algebra involving the reflection operator is revealed. It is shown that in addition to the well-known infinite-dimensional representations related to parabosons, the algebra has also finite-dimensional…
In this article, we give an explicit construction of the simple modules for both non-degenerate and degenerate cyclotomic Hecke-Clifford superalgebras over an algebraically closed field of characteristic not equal to $2$ under certain…
A modular fusion category C allows one to define projective representations of the mapping class groups of closed surfaces of any genus. We show that if all these representations are irreducible, then C has a unique Morita-class of simple…
Noncommutative pfaffians associated with an orthogonal algebra are some special elements of the universal enveloping algebra. In the paper it is suggested to use some pfaffians as raising operators. The images of these pfaffians in the…
The aim of this paper is to gather and (try to) unify several approaches for the modular representation theory of Hecke algebras of type $B$. We attempt to explain the connections between Geck's cellular structures (coming from…
Let $\mathop{\rm CF}\nolimits(\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A})$ denote the vector space of $\mathbb{Q}$-valued constructible functions on a given stack $\mathop{\mathfrak{Obj}\kern .05em}\nolimits_\mathcal{A}$ for an…
In this paper all of the classical constructions of A. Young are generalized to affine Hecke algebras of type A. It is proved that the calibrated irreducible representations of the affine Hecke algebra are indexed by placed skew shapes and…
We construct new extensions of current and diffeomorphism algebras in N>3 dimensions, which are related to the Mickelsson-Faddeev algebra. The result is compatible with Dzhumadil'daev's classification of diffeomorphism cocycles. We also…
We study non-selfadjoint representations of a finite dimensional real Lie algebra $\fg$. To this end we embed a non-selfadjoint representation of $\fg$ into a more complicated structure, that we call a $\fg$-operator vessel and that is…
We give some examples of non-complete invariant affine connections on nilpotent and filiform Lie groups. This permits to describe non-nilpotent faithful representations on the model of filiform n-dimensional Lie algebras and, in particular,…
Inspired by the perspective of Reyes' noncomutative spectral theory, we attempt to develop noncommutative algebraic geometry by introducing ringed coalgebras, which can be thought of as a noncommutative generalization of schemes over a…
We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sewing of surfaces, and in the Minkowskian case we describe CFT…
We establish a quantum cluster algebra structure on the quantum Grothendieck ring of a certain monoidal subcategory of the category of finite-dimensional representations of a simply-laced quantum affine algebra. Moreover, the…
We use the Fock space representation of the quantum affine algebra of type $A^{(2)}_{2n}$ to obtain a description of the global crystal basis of its basic level 1 module. We formulate a conjecture relating this basis to decomposition…
We will present an algebra describing a mixed paraparticle model, known in the bibliography as "The Relative Parabose Set (\textsc{Rpbs})". Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom…
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…
We study the vertex algebras associated with modular invariant representations of affine Kac-Moody algebras at fractional levels, whose simple highest weight modules are classified by Joseph's characteristic varieties. We show that an…
We study which von Neumann algebras can be embedded into uniform Roe algebras and quasi-local algebras associated to a uniformly locally finite metric space $X$. Under weak assumptions, these $\mathrm{C}^*$-algebras contain embedded copies…