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The 3-state Potts model and Rogers-Ramanujan series

Alex Feingold, Antun Milas (2013)

Open Mathematics

We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic A 2(2) -modules, previously discovered by the first author in [Feingold A.J., Some applications of vertex operators to Kac-Moody algebras, In: Vertex Operators in Mathematics and Physics, Berkeley, November 10–17, 1983, Math. Sci. Res. Inst. Publ., 3, Springer, New York, 1985, 185–206]. The key new ingredients are (5,6)Virasoro minimal models and twisted modules for the Zamolodchikov W 3-algebra.

The Brauer category and invariant theory

Gustav I. Lehrer, R. B. Zhang (2015)

Journal of the European Mathematical Society

A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O ( V ) or the symplectic group Sp ( V ) over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...

The duality correspondence of infinitesimal characters

Tomasz Przebinda (1996)

Colloquium Mathematicae

We determine the correspondence of infinitesimal characters of representations which occur in Howe's Duality Theorem. In the appendix we identify the lowest K-types, in the sense of Vogan, of the unitary highest weight representations of real reductive dual pairs with at least one member compact.

The F-method and a branching problem for generalized Verma modules associated to ( Lie G 2 , so ( 7 ) )

Todor Milev, Petr Somberg (2013)

Archivum Mathematicum

The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras Lie G 2 i so ( 7 ) , and generalized conformal so ( 7 ) -Verma modules of scalar type. As a result, we classify the i ( Lie G 2 ) 𝔭 -singular vectors for this class of so ( 7 ) -modules.

The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras

Alexander Rudy (2005)

Open Mathematics

The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.

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