We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of “local system of vertex operators” for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space M has a natural vertex (super)algebra structure with M as a module. Then we prove that for a vertex (operat...

We construct representationsˆπ ¯ r of the quantum algebra U q (sl(n)) labelled by n − 1 complex numbers r i and acting in the space of formal power series of n(n − 1)/2 non-commuting variables. These variables generate a flag manifold of the matrix quantum group SL q (n) which is dual to U q (sl(n)). The conditions for reducibility ofˆπ ¯ r and the procedure for the construction of the q-differ...

We give a group-theoretic interpretation of non-relativistic holography as equivalence between representations of the Schrödinger algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-tobulk operators for which we first construct the two-point Green function in the bulk. Further we show that these operators and the bulk-to-boundary oper...

We conjecture a geometrical form of the Paley–Wiener theorem for the Dunkl transform and prove three instances thereof, by using a reduction to the one-dimensional even case, shift operators, and a limit transition from Opdam’s results for the graded Hecke algebra, respectively. These Paley– Wiener theorems are used to extend Dunkl’s intertwining operator to arbitrary smooth functions. Furtherm...

Following Beurling’s theorem the natural compressions of multiplication operator in classical $$L^2$$ space are to model spaces and their orthogonal complements. Here, two possibly different considered, hence asymmetric truncated Toeplitz dual operators investigated. The main purpose paper is characterize which intertwine unilateral shift.