6,400 research outputs found
Realising Intensional S4 and GL Modalities
No full textThere have been investigations into type-theoretic foundations for metaprogramming, notably Davies and Pfenning’s (2001) treatment in S4 modal logic, where code evaluating to values of type A is given the modal type Code A (□A in the original paper). Recently Kavvos (2017) extended PCF with Code A and intensional recursion, understood as the deductive form of the GL (Gödel-Löb) axiom in provability logic, but the resulting type system is logically inconsistent. Inspired by staged computation, we observe that a term of type Code A is, in general, code to be evaluated in a next stage, whereas S4 modal type theory is a special case where code can be evaluated in the current stage, and the two types of code should be discriminated. Consequently, we use two separate modalities ⊠ and □ to model S4 and GL respectively in a unified categorical framework while retaining logical consistency. Following Kavvos’ (2017) novel approach to the semantics of intensionality, we interpret the two modalities in the P-category of assemblies and trackable maps. For the GL modality □ in particular, we use guarded type theory to articulate what it means by a “next” stage and to model intensional recursion by guarded recursion together with Kleene’s second recursion theorem. Besides validating the S4 and GL axioms, our model better captures the essence of intensionality by refuting congruence (so that two extensionally equal terms may not be intensionally equal) and internal quoting (both A → □A and A → ⊠A). Our results are developed in (guarded) homotopy type theory and formalised in Agda
to durancin GL
No full textTarget cell recognition is an important issue in the realization of bacteriocin's activity. In this report, we provide genetic and biochemical evidence of durancin GL, a new bacteriocin produced by Enterococcus durans 41D, and use ⅡC subunit in the mannose phosphotransferase system (Man-PTS) of Listeria monocytogenes as target/receptor. First, the L. monocytogenes mutants with Man-PTS IIC or IID deletion were constructed with the vector pHoss1. Then, the utilization of glucose and mannose and the sensitivity to durancin GL of the mutant strains were investigated. Afterward, the interactions between durancin GL and the subunits of IIC or IID in Man-PTS of L. monocytogenes were characterized by yeast two-hybrid system. The results showed that the L. monocytogenes mutants with either IIC or IID deletion were not only resistant to durancin GL, but also their absorption and utilization of glucose and mannose were not disturbed by the presence of durancin GL. Finally, in situ detection of the interaction between durancin GL and Man-PTS subunits of IIC or IID by yeast two-hybrid system revealed that there was a strong interaction between durancin GL and Man-PTS subunit IIC. However, the interaction between durancin GL and Man-PTS subunit IID was not present or weak. Based on the experimental evidence above, the Man-PTS subunit IIC is responsible for the sensitivity of L. monocytogenes to bacteriocin durancin GL
On Deligne's conjecture for certain automorphic L-functions for GL(3)xGL(2) and GL(4)
No full textWe prove Deligne's conjecture for certain automorphic L-functions for GL(3)×GL(2) and GL(4). The proof is based on rationality results for central critical values of triple product L-functions, which follow from establishing explicit Ichino's formulae for trilinear period integrals for Hilbert cusp forms on totally real étale cubic algebras over Q.補正完
Globalization of Distinguished Supercuspidal Representations of GL(n)
No full textAn irreducible supercuspidal representation of = GL(n, ), where is a nonarchimedean local field of characteristic zero, is said to be “distinguished” by a subgroup of and a quasicharacter of if Hom(, ) ≠ 0. There is a suitable global analogue of this notion for an irreducible, automorphic, cuspidal representation associated to GL(n). Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. Applications to the theory of distinguished supercuspidal representations are provided
Restriction of Representations of GL (n + 1, ℂ) to GL (n, ℂ) and Action of the Lie Overalgebra
No full textConsider a restriction of an irreducible finite dimensional holomorphic representation of GL(n+1,C) to the subgroup GL(n,C). We write explicitly formulas for generators of the Lie algebra gl(n+1) in the direct sum of representations of GL(n,C). Nontrivial generators act as differential-difference operators, the differential part has order n − 1, the difference part acts on the space of parameters (highest weights) of representations. We also formulate a conjecture about unitary principal series of GL(n,C).© The Author(s) 201
The Balanced Voronoi Formulas for
No full textAbstract
In this article, we show how the Voronoi summation formula of [13] can be rewritten to incorporate hyper-Kloosterman sums of various dimensions on both sides. This generalizes a formula for with ordinary Kloosterman sums on both sides that was used in [1] to prove nonvanishing of GL(4) -functions by GL(2)-twists, and later by the second-named author in [16].</jats:p
Bethe Vectors for Composite Models with gl(2|1) and gl(1|2) Supersymmetry
No full textSupersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors in the composite models with supersymmetry based on the super-Yangians Y[gl(2|1)] and Y[gl(1|2)] are derived.The author wants to express his gratitude to N.A. Slavnov for the proposal to investigate this
topic and discussions. He thanks also to S. Pakuliak for discussions and to A.P. Isaev and
C. Burd´ık for their support. The work of the author has been supported by the Grant Agency ˇ
of the Czech Technical University in Prague, grant No. SGS15/215/OHK4/3T/14, and by the
Grant of the Plenipotentiary of the Czech Republic at JINR, Dubna
Combinatorial results on (1,2,1,2)-avoiding -orbit closures on
No full text35 pages, 18 figuresInternational audienceUsing recent results of the second author which explicitly identify the "-avoiding" -orbit closures on the flag manifold as certain Richardson varieties, we give combinatorial criteria for determining smoothness, lci-ness, and Gorensteinness of such orbit closures. (In the case of smoothness, this gives a new proof of a theorem of W.M. McGovern.) Going a step further, we also describe a straightforward way to compute the singular locus, the non-lci locus, and the non-Gorenstein locus of any such orbit closure. We then describe a manifestly positive combinatorial formula for the Kazhdan-Lusztig-Vogan polynomial in the case where corresponds to the trivial local system on a -avoiding orbit closure and corresponds to the trivial local system on any orbit contained in . This combines the aforementioned result of the second author, results of A. Knutson, the first author, and A. Yong, and a formula of Lascoux and Sch\"{u}tzenberger which computes the ordinary (type ) Kazhdan-Lusztig polynomial whenever is cograssmannian
Hopf algebra and the duality operation for
No full textIn this paper we study the space of complex invariant functions on , through a Hopf algebra viewpoint. First, we consider a variant notion of Zelevinsky\u27s PSH algebra defined over the real numbers . In particular, we show that two specific -lattices inside the complex Hopf algebra are real PSH algebras, and that they do not descend to . Then, among consequences, we prove that every element in is a linear combination of Harish-Chandra inductions of Kawanaka\u27s pre-cuspidal functions, and give a conceptual characterisation of duality operation for , which in turn allows us to give a new proof of a classical result of Kawanaka.15 pages; 2nd ver: corrected the (truncated) abstract presented in the arXiv pag
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