TY - JOUR
AB - Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell.
AU - Brown, Adam
AU - Romanov, Anna
ID - 8773
IS - 1
JF - Proceedings of the American Mathematical Society
KW - Applied Mathematics
KW - General Mathematics
SN - 0002-9939
TI - Contravariant forms on Whittaker modules
VL - 149
ER -
TY - JOUR
AB - Li-Nadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti geometric Langlands conjecture of Ben-Zvi-Nadler in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds in the natural generality of reflection groups in Euclidean or hyperbolic space. As a corollary, we give an expression of the centralizer of a finite order element in a reflection group using homotopy theory.
AU - Li, Penghui
ID - 6986
IS - 11
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
TI - A colimit of traces of reflection groups
VL - 147
ER -
TY - JOUR
AB - In this note, we consider the dynamics associated to a perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of ``micro-diffusion'': under generic assumptions on $ h$ and $ f$, there exists an orbit of the system for which the drift of its action variables is at least of order $ \sqrt {\varepsilon }$, after a time of order $ \sqrt {\varepsilon }^{-1}$. The assumptions, which are essentially minimal, are that there exists a resonant point for $ h$ and that the corresponding averaged perturbation is non-constant. The conclusions, although very weak when compared to usual instability phenomena, are also essentially optimal within this setting.
AU - Bounemoura, Abed
AU - Kaloshin, Vadim
ID - 8495
IS - 4
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
TI - A note on micro-instability for Hamiltonian systems close to integrable
VL - 144
ER -