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12 papers · 1 filter
Bidirectional coherent classical communication
Aram W. Harrow, Debbie W. Leung
A unitary interaction coupling two parties enables quantum communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff be…
A combinatorial proof of the Rogers-Ramanujan and Schur identities
Cilanne Boulet, Igor Pak
We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direct bij…
The compactified Picard scheme of the compactified Jacobian
Eduardo Esteves, Steven Kleiman
Let C be an integral projective curve in any characteristic. Given an invertible sheaf L on C of degree 1, form the associated Abel map A_L : C -> P, which maps C into its compacti…
Irreducible Modules over Finite Simple Lie Pseudoalgebras I. Primitive Pseudoalgebras of Type W and S
B. Bakalov, A. D'Andrea, V. G. Kac
One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal alge…
Unipotent variety in the group compactification
Xuhua He
The unipotent variety of a reductive algebraic group plays an important role in the representation theory. In this paper, we will consider the closure $\bar{\Cal U}$ of the uni…
The area of cyclic polygons: Recent progress on Robbins' Conjectures
Igor Pak
In his works [R1,R2] David Robbins proposed several interrelated conjectures on the area of the polygons inscribed in a circle as an algebraic function of its sides. Most recently,…