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

Polynomial Tau-functions of the KP, BKP, and the s-Component KP Hierarchies

We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero mode of an appropriate combinatorial generating function. As an application, we obtain explicit formulas for all polynomial tau-functions of these hierarchies in terms of Schur polynomials and Q-Schur polynomials respectively. We also obtain formulas for polynomial tau-functions of the reductions of the s-component KP hierarchy associated to partitions in s parts.Comment: 28 page

Metaplectic Ice

We study spherical Whittaker functions on a metaplectic cover of GL(r + 1) over a nonarchimedean local eld using lattice models from statistical mechanics. An explicit description of this Whittaker function was given in terms of Gelfand-Tsetlin patterns in [5, 17], and we translate this description into an expression of the values of the Whittaker function as partition functions of a six- vertex model. Properties of the Whittaker function may then be expressed in terms of the commutativity of row transfer matrices potentially amenable to proof using the Yang-Baxter equation. We give two examples of this: rst, the equivalence of two di erent Gelfand-Tsetlin de nitions, and second, the e ect of the Weyl group action on the Langlands parameters. The second example is closely connected with another construction of the metaplectic Whittaker function by averaging over a Weyl group action [9, 10]

Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established

From Higher Spins to Strings: A Primer

A contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen, this introductory article is a pedagogical account of higher-spin fields and their connections with String Theory. We start with the motivations for and a brief historical overview of the subject. We discuss the Wigner classifications of unitary irreducible Poincar\'e-modules, write down covariant field equations for totally symmetric massive and massless representations in flat space, and consider their Lagrangian formulation. After an elementary exposition of the AdS unitary representations, we review the key no-go and yes-go results concerning higher-spin interactions, e.g., the Velo-Zwanziger acausality and its string-theoretic resolution among others. The unfolded formalism, which underlies Vasiliev's equations, is then introduced to reformulate the flat-space Bargmann-Wigner equations and the AdS massive-scalar Klein-Gordon equation, and to state the "central on-mass-shell theorem". These techniques are used for deriving the unfolded form of the boundary-to-bulk propagator in $AdS_4$, which in turn discloses the asymptotic symmetries of (supersymmetric) higher-spin theories. The implications for string-higher-spin dualities revealed by this analysis are then elaborated.Comment: 106 pages, 2 figures. Contribution to the collection of reviews "Introduction to Higher Spin Theory" edited by S. Fredenhagen. V2: Typos corrected, acknowledgements and references adde

Arts Immersion: Using the arts as a language across the primary school curriculum

Abstract: Australia’s national arts curriculum has potential to realise the following benefits: cognitive, social, affective and curricular. This curriculum is designed for generalist and special arts teachers, but its delivery may be hindered by the prioritisation of high-stakes-tested disciplines and pedagogies, and reduced government funding to arts education across school and tertiary sectors. This may lead to a lack of opportunities to build teacher capacity in arts education, and diminished support for arts education in terms of time allocation and resourcing. The notion of ‘silos’, where the separation of teaching practices persists between teachers of different disciplines, discourages meaningful interdisciplinary collaboration and can promote less effective models of arts integration. Arts education embodies a range of intelligences and semiotic systems providing for inclusive curricula and educational equity. Arts Immersion is a proposed response to these factors, intended to be implemented through democratic generalist and arts specialist team-teaching in primary schools

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book