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Showing 1 to 9 of 9 for “"Verma module"”.
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Homomorphisms of semi-holonomic verma modules : an exceptional case.
Verma modules play an important part in the theory of invariant operators on homogeneous spaces. If G is a semisimple Lie group and P a parabolic subgroup of G, then there is often a differential geometry for which the homogeneous space G/P represents the flat model. An example is conformal …
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On the signature of the Shapovalov form
… problem of classifying the Harish-Chandra modules admitting a positive definite invariant Hermitian form. Finding a formula for the signature of the Shapovalov form is a related problem which may be a necessary first step in such a classification. A Verma module may admit an invariant …
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On representations of rational Cherednik algebras
… formula for the Gaussian inner product on a Verma module in the rational Cherednik category O. At real parameter values, the restriction of K to the regular locus in the real reflection representation can be interpreted as an analytic function taking values in Hermitian forms, invariant under …
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The fine structure of translation functors, the triangle function and a construction of R-matrices
… e in E_{ <br>u} nonzero. <br>Let M( au) be the Verma module with highest weight au and v_{ au} the canonical <br>generator. <br>We investigate the projection of e otimes v_{ au} in E otimes M( au) on the <br>central character chi( au + <br>u). This is a rational function in au and we …
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Unitary Irreducible Highest Weight Modules of su(2,1) of Highest Weight λ - ρ Where λ is Integral Regular
… is the unique irreducible quotient of the Verma module M(x(−λ)) of highest weight x(−λ) − ρ. One of the most important open problems in Mathematics is called The Unitary Dual Problem: classify the irreducible unitary representations of a group. This was introduced in the 1930s by Israel …
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The Frobenius direct image of line bundles and the structure of representations
… representations of G which are dual to the Weyl modules. In this thesis, our central object of study is the direct image of the induced line bundles under the Frobenius morphism. I.e., $F\sb\*{\cal L}$($\lambda$). We study the homogeneous sheaf structure of $F\sb\*{\cal L}$($\lambda$) in the …
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Indices for Supersymmetric Quantum Field Theories in Four Dimensions
… shortening conditions, we compute the associated Verma module characters, from which we can extract the index in the appropriate limit. This approach only provides us with the free field theory limit for the index and does not account for the values of the $R$-charges away from free field …
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Geometric aspects of three dimensional N = 4 gauge theories
… blocks realise characters of lowest weight Verma modules of the Higgs and Coulomb branch chiral rings acting on boundary local operators. We study the geometric interpretation of the twisted index factorisation in particular and demonstrate a relationship between the twisted index and the …
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On Vertex Operator Algebras of Affine Type at Admissible Levels
… singular vectors which generate the maximal submodules, with respect to which these VOAs appear as irreducible quotients, and therefore a substantial part of the text is devoted to this matter. We study in particular the simple VOAs associated to affine sl(3, C) with half-integer admissible …