A study of the introduction of ions into the region of strong fields within a quadrupole mass spectrometer Quarterly progress report, 17 May - 17 Aug. 1966

Introduction of ions into region of strong fields within quadrupole mass filte

A study of the introduction of ions into the region of strong fields within a quadrupole mass spectrometer Second quarterly progress report, 17 Nov. 1965 - 17 Feb. 1966

Ion introduction into strong fields of quadrupole mass spectromete

A study of the introduction of ions into the region of strong fields within a quadrupole mass spectrometer Third quarterly progress report, 17 Feb. - 17 May 1966

Ion introduction into high intensity electric fields within quadrupole mass spectrometer using stainless steel ro

Quadrupole mass spectrometer Final report

Quadrupole mass spectrometer operation in presence of high background pressure of hydroge

Astronaut breath analyzer Final report

Miniature vacuum system for use as breath analyzer in astronaut space sui

Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation