223,139 research outputs found
The Wronski map and shifted tableau theory
The Mukhin-Tarasov-Varchenko Theorem, conjectured by B. and M. Shapiro, has a
number of interesting consequences. Among them is a well-behaved correspondence
between certain points on a Grassmannian - those sent by the Wronski map to
polynomials with only real roots - and (dual equivalence classes of) Young
tableaux.
In this paper, we restrict this correspondence to the orthogonal Grassmannian
OG(n,2n+1) inside Gr(n,2n+1). We prove that a point lies on OG(n,2n+1) if and
only if the corresponding tableau has a certain type of symmetry. From this we
recover much of the theory of shifted tableaux for Schubert calculus on
OG(n,2n+1), including a new, geometric proof of the Littlewood-Richardson rule
for OG(n,2n+1).Comment: 11 pages, color figures, identical to v1 but metadata correcte
On a conjecture by Naito-Sagaki: Littelmann paths and Littlewood-Richardson Sundaram tableaux
We prove a special case of a conjecture of Naito-Sagaki about a branching
rule for the restriction of irreducible representations of
to . The
conjecture is in terms of certain Littelmann paths, with the embedding given by
the folding of the type Dynkin diagram. We propose and motivate an
approach to the conjecture in general, in terms of Littlewood-Richardson
Sundaram tableaux.Comment: 13 pages. Comments welcom
Holographic Thermal Helicity
We study the thermal helicity, defined in arXiv:1211.3850, of a conformal
field theory with anomalies in the context of AdS/CFT. To do
so, we consider large charged rotating AdS black holes in the
Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant
using fluid/gravity expansion. We compute the anomaly-induced current and
stress tensor of the dual CFT in leading order of the fluid/gravity derivative
expansion and show their agreement with the field theoretical replacement rule
for the thermal helicity. Such replacement rule is reflected in the bulk by new
replacement rules obeyed by the Hall currents around the black hole.Comment: 20 pages + 47 pages of appendices ; v2: minor correction
Collective excitations of a trapped Bose-condensed gas
By taking the hydrodynamic limit we derive, at , an explicit solution of
the linearized time dependent Gross-Pitaevskii equation for the order parameter
of a Bose gas confined in a harmonic trap and interacting with repulsive
forces. The dispersion law for the
elementary excitations is obtained, to be compared with the prediction
of the noninteracting harmonic oscillator model.
Here is the number of radial nodes and is the orbital angular
momentum. The effects of the kinetic energy pressure, neglected in the
hydrodynamic approximation, are estimated using a sum rule approach. Results
are also presented for deformed traps and attractive forces.Comment: uuencoded file including 12 pages REVTEX and 1 figur
K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
We present a proof of a Littlewood–Richardson rule for the K-theory of odd orthogonal Grassmannians OG(n, 2n+1), as conjectured by Thomas–Yong (2009). Specifically, we prove that rectification using the jeu de taquin for increasing shifted tableaux introduced there, is well-defined and gives rise to an associative product. Recently, Buch–Ravikumar(2012) proved a Pieri rule for OG(n, 2n+1) that confirms a special case of the conjecture. Together, these results imply the aforementioned conjecture
- …