Yi - Wei Sun

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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 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)
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)