Faculty recital: Harvey Pittel and Jeffrey Hellmer, November 4, 1994

This is the concert program of the Faculty recital: Harvey Pittel and Jeffrey Hellmer performance on Friday, November 4, 1994 at 8:00 p.m., at the Boston University Concert Hall, 855 Commonwealth Avenue, Boston, Massachusetts. Works performed were Concerto Saint Marco by Tomaso Albinoni, Tableaux de Provence by Paule Maurice, Sonata for Alto Saxophone and Piano, Op. 19 by Paul Creston, Wings for Solo Saxophone by Joan Tower, Vocalise by Sergei Rachmaninoff, "Acrostic Song" from Final Alice by David Del Tredici, and Introduction and Variations on "La Carnaval de Venise" by Jules Demersseman. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

On Cellular Algebras with Jucys Murphy Elements

We study analogues of Jucys-Murphy elements in cellular algebras arising from repeated Jones basic constructions. Examples include Brauer and BMW algebras and their cyclotomic analogues.Comment: Improved and reorganized exposition. Some new result

The Algebra of Binary Search Trees

We introduce a monoid structure on the set of binary search trees, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion. This leads to a new construction of the algebra of Planar Binary Trees of Loday-Ronco, defining it in the same way as Non-Commutative Symmetric Functions and Free Symmetric Functions. We briefly explain how the main known properties of the Loday-Ronco algebra can be described and proved with this combinatorial point of view, and then discuss it from a representation theoretical point of view, which in turns leads to new combinatorial properties of binary trees.Comment: 49 page

A class of overdetermined systems defined by tableaux: involutiveness and Cauchy problem

This article addresses the question of involutiveness and discusses the initial value problem for a class of overdetermined systems of partial differential equations which arise in the theory of integrable systems and are defined by tableaux.Comment: 14 page

A geometric Littlewood-Richardson rule

We describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties. There are no restrictions on the base field, and all multiplicities arising are 1; this is important for applications. This rule should be seen as a generalization of Pieri's rule to arbitrary Schubert classes, by way of explicit homotopies. It has a straightforward bijection to other Littlewood-Richardson rules, such as tableaux, and Knutson and Tao's puzzles. This gives the first geometric proof and interpretation of the Littlewood-Richardson rule. It has a host of geometric consequences, described in the companion paper "Schubert induction". The rule also has an interpretation in K-theory, suggested by Buch, which gives an extension of puzzles to K-theory. The rule suggests a natural approach to the open question of finding a Littlewood-Richardson rule for the flag variety, leading to a conjecture, shown to be true up to dimension 5. Finally, the rule suggests approaches to similar open problems, such as Littlewood-Richardson rules for the symplectic Grassmannian and two-flag varieties.Comment: 46 pages, 43 figure