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Journals and Conferences
We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of Uq(gln). In the GelfandTsetlin basis, we show that diagonal matrix elements of such intertwiners are given by application of Macdonald’s operators to a simple kernel. An… (More)
The waiting time for given bandwidth is considered as one of the most important performance metrics of video-on-demand broadcasting schemes. It is known that, if the available bandwidth is c times the display rate of a video, then 1/(e<sup>c</sup> -1) is the tight lower bound on the maximum waiting time normalized by the video duration. The best general… (More)
We provide Harish-Chandra type formulas for the multivariate Bessel functions and HeckmanOpdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization of Macdonald polynomials as traces of intertwiners of quantum groups given by Etingof-Kirillov Jr. in [EK94].… (More)
We consider large Aloha systems in which the mean arrival rate and channel bandwidth tend to infinity with their ratio kept a constant. In such large Aloha systems the channel uncertainty is captured by a notion of effective interference and thus the packet success probability depends only on the mean composite arrival per dimension and is independent of… (More)
1.1 Symplectic structure on the cotangent bundle Let G be a semisimple algebraic group with Lie algebra g. Fix a Borel subgroup B of G, and let B = G/B be the corresponding flag variety. The cotangent bundle T ∗B comes equipped with symplectic form ω = dλ defined as follows. For x ∈ B and α ∈ T ∗ xB, let π : T ∗B → B be the projection and π∗ : TαT ∗B → TxB… (More)
2. A configuration of 4027 points in the plane is called Colombian if it consists of 2013 red points and 2014 blue points, and no three of the points of the configuration are collinear. By drawing some lines, the plane is divided into several regions. An arrangement of lines is good for a Colombian configuration if the following two conditions are… (More)
where we view Gm(S) as the subgroup of invertible scalars in GLn(S). Define PGLn = s ◦ P̃GLn to be its sheafification (taken in the sense of Problem 8 on PS 2). Our goal will be to show that PGLn is an affine group scheme that represents automorphisms of projective space in the sense that PGLn(S) ' AutS(S × Pn−1). Before we begin, we require some… (More)
These are notes for a talk in the MIT-Northeastern Spring 2015 Graduate Representation Theory Seminar. The main source is [BR14].
In this paper, we study representations of the rational Cherednik algebra associated to the complex reflection group G4. In particular, we classify the irreducible finite dimensional representations and compute their characters.