Related papers: Braided differential structure on Weyl groups, qua…

On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…

For the algebraic group $SL_{l+1}(\mathbb{C})$ we describe a system of positive roots associated to conjugacy classes in its Weyl group. Using this we explicitly describe the algebra of regular functions on certain transverse slices to…

Let $V$ be a braided vector space of diagonal type. Let $\mathfrak B(V)$, $\mathfrak L^-(V)$ and $\mathfrak L(V)$ be the Nichols algebra, Nichols Lie algebra and Nichols braided Lie algebra over $V$, respectively. We show that a monomial…

This is a noncommutative version of the previous work entitled "Deformation Expression for Elements of Algebras (I)." In general in a noncommutative algebra, there is no canonical way to express elements in univalent way, which is often…

The paper is the sequel to q-alg/9704011. We extend the Drinfeld-Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic deformation of the Lie bialgebra…

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption…

In this paper, as a generalization of Kirillov's orbit theory, we explore the relationship between the dressing orbits and irreducible *-representations of the Hopf C*-algebras (A,\Delta) and (\tilde{A}, \tilde{\Delta}) we constructed…

It has long been known that the differential operator $D$ represents a typical examples of unbounded operators in many Banach spaces including the classical Fock spaces, the Fock--Sobolev spaces, and the generalized Fock spaces where the…

We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new invariants such as real roots. The crucial ingredient is a `reflection' in the class of such Nichols algebras. We conclude the classifications of…

We consider decompositions of digraphs into edge-disjoint paths and describe their connection with the $n$-th Weyl algebra of differential operators. This approach gives a graph-theoretic combinatorial view of the normal ordering problem…

The generalized diamond group is the semi-direct product $G$ of the abelian group ${\mathbb R}^m$ by the $(2n+1)$-dimensional Heisenberg group $H_n$. We construct the generic representations of $G$ on the Fock space by extending those of…

It is known that there exists an order isomorphism between the Weyl group orbit through a minuscule weight of a simply-laced finite-dimensional simple Lie algebra and the set of all order filters in a self-dual connected d-complete poset.…

Invited talk at the International Symposium on Generalized Symmetries in Physics at the Arnold-Sommerfeld-Institute, Clausthal, Germany, July 26 -- July 29, 1993. This talk reviews results on the structure of algebras consisting of…

For a symmetrizable Kac-Moody algebra the category of admissible representations is an analogue of the category of finite dimensional representations of a semisimple Lie algebra. The monoid associated to this category and the category of…

We define the q-deformed Gelfand-Dickey bracket on the space of q-pseudodifference symbols which agrees with the Poisson Virasoro algebra of E.Frenkel and N.Reshetikhin and its generalizations and prove its uniqueness (in a natural class of…

In this paper we push forward results on the invariant ${\cal F}$-module of a virtual knot investigated by the first named author where ${\cal F}$ is the algebra with two invertible generators $A,B$ and one relation…

This paper is devoted to the calculation of Batalin-Vilkovisky algebra structures on the Hochschild cohomology of skew Calabi-Yau generalized Weyl algebras. We firstly establish a Van den Bergh duality at the level of complex. Then based on…

In the paper we study the algebroid A of the groupoid of partially invertible elements over the lattice of orthogonal projections of a $W^*$-algebra. In particular the complex analytic manifold structure of these objects is investigated.…

We classify subalgebras of a ring of differential operators which are big in the sense that the extension of associated graded rings is finite. We show that these subalgebras correspond, up to automorphisms, to uniformly ramified finite…

We establish several results concerning tensor products, q-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the root of unity setting. In the generic case, a Weyl…