Related papers: Refined product formulas for Tamari intervals
We introduce formulae of Frobenius-Schur indicators of simple objects of Tambara-Yamagami categories. By using techniques of the Fourier transform on finite abelian groups, we study some arithmetic properties of indicators.
We obtain a family of explicit "polyhedral" combinatorial expressions for multiplicities in the tensor product of two simple finite-dimensional modules over a complex semisimple Lie algebra. Here "polyhedral" means that the multiplicity in…
We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary we obtain a simple product formula for the characteristic polynomial of alternating…
We establish the Hao-Ng isomorphism for generalized gauge actions of locally compact abelian groups on product systems over abelian lattice orders and we then use it to explore Takai duality in this context. As an application we generalize…
The Tamari lattice, defined on Catalan objects such as binary trees and Dyck paths, is a well-studied poset in combinatorics. It is thus natural to try to extend it to other families of lattice paths. In this article, we fathom such a…
Given any poset $P$ and chain $\phi$ in $P$, we define the $(P,\phi)$-Tamari lattice. We study in depth these lattices and prove in particular that they are join-semidistributive, join-congruence uniform and left modular. We prove that the…
We show that certain spaces of vector valued modular forms are isomorphic to spaces of scalar valued modular forms whose Fourier coefficients are supported on suitable progressions. As an application we give a very explicit description of…
In this paper the approach to obtaining nonrecurrent formulas for some recursively defined sequences is illustrated. The most interesting result in the paper is the formula for the solution of quadratic map-like recurrence. Also, some…
Motivated by the behavior of the trace pairing over tame cyclic number fields, we introduce the notion of tame lattices. Given an arbitrary non-trivial lattice $\mathcal{L}$ we construct a parametric family of full-rank sub-lattices…
In this paper, we define and prove basic properties of complement polyhedral product spaces, dual complexes and polyhedral product complexes. Then we compute the universal algebra of polyhedral product complexes under certain split…
We present the basic concepts of tensor products of vector spaces, emphasizing linear algebraic and combinatorial techniques as needed for applied areas of research. The topics include (1) Introduction; (2) Basic multilinear algebra; (3)…
We use the remark that, through Bargmann-Fock representation, diagonal operators of the Heisenberg-Weyl algebra are scalars for the Hadamard product to give some properties (like the stability of periodic fonctions) of the Hadamard product…
We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing explicit character computations.
This paper is devoted to constructing simple modules of the planar Galilean conformal algebra. We study the tensor products of finitely many simple $\mathcal{U}(\mathcal{H})$-free modules with an arbitrary simple restricted module, where…
Product Lagrangian tori in standard symplectic space $R^{2n}$ were classified up to symplectomorphism in [Che96]. We extend this classification to tame symplectically aspherical symplectic manifolds. We show by examples that the asphericity…
We construct canonical bases in tensor products of several lowest and highest weight integrable modules, generalizing Lusztig's work.
Some basic features of the simultaneous inclusion of discrete fibrations and discrete opfibrations in categories over a base category X are considered. In particular, we illustrate the formulas (|P)x = ten(x/X,P) ; (P|)x = hom(X/x,P) which…
We give a new proof of Theorem 6 in [L. Qiu and X. Zhan, On the span of Hadamard products of vectors, Linear Algebra Appl. 422 (2007) 304--307].
We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a…
In this paper the analogy between differential forms arising from integrals in additive calculus and forms arising from the integrals in product calculus is investigated. It is found that with an appropriate definition of scalar…