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Commuting families in Hecke and Temperley-Lieb algebras
Abstract
We define analogs of the Jucys-Murphy elements for the affine Temperley-Lieb algebra and give their explicit expansion in terms of the basis of planar Brauer diagrams. These Jucys-Murphy elements are a family of commuting elements in the affine Temperley-Lieb algebra, and we compute their eigenvalues on the generic irreducible representations. We show that they come from Jucys-Murphy elements in the affine Hecke algebra of type A, which in turn come from the Casimir element of the quantum group . We also give the explicit specializations of these results to the finite Temperley-Lieb algebra.12
Otis Murphy, saxophone and Haruko Murphy, piano, January 27, 2015
This is the concert program of the Otis Murphy, saxophone and Haruko Murphy, piano performance on Tuesday, January 27, 2015 at 8:00 p.m., at the Marshall Room, 855 Commonwealth Avenue. Works performed were "A Jerome Kern Songbook" (arr. Martino) by Jerome Kern, "The Bees" by Antonio Pasculli (arr. Tse), Sonata, Opus 116 by Camille Saint-Saëns, Rhapsody for Alto Saxophone and Piano by André Waignein, Vocalise, Op. 34 No. 14 by Sergei Rachmaninoff (arr. Murphy), and "Carmen Fantasy" from the Opera by G. Bizet by François Borne (arr. Roth/Meylan). Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund
Jucys-Murphy elements and a presentation for partition algebras
We give a new presentation for the partition algebras. This presentation was
discovered in the course of establishing an inductive formula for the partition
algebra Jucys-Murphy elements defined by Halverson and Ram [European J. Combin.
26 (2005), 869-921]. Using Schur-Weyl duality we show that our recursive
formula and the original definition of Jucys-Murphy elements given by Halverson
and Ram are equivalent. The new presentation and inductive formula for the
partition algebra Jucys-Murphy elements given in this paper are used to
construct the seminormal representations for the partition algebras in a
separate paper.Comment: 39 pages, 9 figures. Typos corrected and editorial changes made from
v1-3. The final publication is available at springerlink.co
Letter of Appreciation: Peter Murphy Retires after a Lifetime of Dedication as Counsel to the Commandant of the Marine Corps
This letter reflects upon the retirement of Peter Murphy after 20 years of service as counsel to the commandant of the Marine Corps. Chief Judge Baker discusses Peter Murphy’s moral courage, common sense, and unflinching dignity while serving as counsel. He relates how Murphy has an abiding commitment to the great institutions of his life and of our lives: the rule of law, the military, and the Marine Corps
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