The Contragredient April 16
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Classification of finite-growth contragredient Lie superalgebras
A contragredient Lie superalgebra is a superalgebra defined by a Cartan matrix. In general, a contragredient Lie superalgebra is not finite dimensional, however it has a natural Z-grading by finite dimensional components. A contragredient Lie superalgebra has finite growth if the dimensions of these graded components depend polynomially on the degree. We discuss the classification of finite-gro...
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Recently, Ash, Pollack and Soares described Galois representations with image isomorphic to GL3(F2), and computationally demonstrated a connection to arithmetic cohomology classes with predictable coefficient modules. In some cases, they did not distinguish between contragredient representations for which the predicted coefficient modules are different. In this paper, we distinguish between the...
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0.1. Let g be a complex finite-dimensional contragredient Lie superalgebra. These algebras were classified by V. Kac in [K1] and the list (excluding Lie algebras) consists of four series: A(m|n), B(m|n), C(m), D(m|n) and the exceptional algebrasD(2, 1, a), F (4), G(3). The finite-dimensional contragredient Lie superalgebras with zero Killing form (or, equivalently, with dual Coxeter number equa...
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We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of p-adic analytic group G. A naive contragredient does not exist. As a best approximation, we construct an involutive “duality” functor from the bounded derived category of modules over the distribution algebra of G with coadmissible cohomology to itself. on the subcateg...
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We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...
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