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Conformal embeddings of affine vertex algebras in minimal W-algebras II: decompositions

Monday September 11th, 2017 Rafael Mrđen 0

Authors: Dražen Adamović, Victor G. Kac, Pierluigi Möseneder Frajria, Paolo Papi, Ozren Perše Japanese Journal of Mathematics, September 2017, Volume 12, Issue 2, pp 261–315. Abstract: We present methods for computing the explicit decomposition of the minimal simple affine W-algebra  as a module for its maximal affine subalgebra  at a conformal level k, that is, whenever the Virasoro vectors of  and  coincide. A particular emphasis […]

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On principal realization of modules for the affine Lie algebra A_1^{(1)} at the critical level

Wednesday April 12th, 2017 Rafael Mrđen 0

Abstract: We present complete realization of irreducible -modules at the critical level in the principal gradation. Our construction uses vertex algebraic techniques, the theory of twisted modules and representations of Lie conformal superalgebras. We also provide an alternative Z-algebra approach to this construction. All irreducible highest weight -modules at the […]

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There Are Infinitely Many Rational Diophantine Sextuples

Saturday March 18th, 2017 Rafael Mrđen 0

A rational Diophantine m-tuple is a set of m non zero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, […]

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On Free Field Realizations of W(2,2)-Modules

Tuesday December 6th, 2016 Rafael Mrđen 0

Abstract The aim of the paper is to study modules for the twisted Heisenberg-Virasoro algebra  at level zero as modules for the -algebra by using construction from [J. Pure Appl. Algebra 219(2015), 4322-4342, arXiv:1405.1707]. We prove that the irreducible highest weight -module is irreducible as -module if and only if it has […]