Proof of the Parthasarathy-Ranga Rao-Varadarajan conjecture
From MaRDI portal
Publication:1118020
DOI10.1007/BF01393689zbMath0668.17008WikidataQ123251819 ScholiaQ123251819MaRDI QIDQ1118020
Publication date: 1988
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/143591
flag manifoldtensor productshighest weightsemisimple Lie algebraline bundlesvanishing theoremcomposition factor
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representation theory for linear algebraic groups (20G05) Homological methods in Lie (super)algebras (17B55) Simple, semisimple, reductive (super)algebras (17B20)
Related Items
Cup products of line bundles on homogeneous varieties and generalized PRV components of multiplicity one, Unnamed Item, Filtrations of $G$-modules, Embeddings of semisimple complex Lie groups and cohomological components of modules, Triangulations and Severi Varieties, Unnamed Item, Standard modules and standard modules of level one, Filtrations of B-modules, Twisted Dirac operators and generalized gradients, Equidimensionality of convolution morphisms and applications to saturation problems., Strongly multiplicity free modules for Lie algebras and quantum groups, A study of Kostant-Kumar modules via Littelmann paths, Perfect submonoids of dominant weights, Kronecker products, minuscule representations, and polynomial identities, PRV for the fusion product, the case \(\lambda \gg \mu \), Normality and smoothness of simple linear group compactifications, Yangians, integrable quantum systems and Dorey's rule, Unnamed Item, Trianguloids and triangulations of root polytopes, The saturation problem for refined Littlewood-Richardson coefficients, A decomposition theorem for Demazure crystals., Moment polytopes, semigroup of representations and Kazarnovskii's theorem, Line bundles on \(G\)-Bott-Samelson-Demazure-Hansen varieties, Dorey's rule and the \(q\)-characters of simply-laced quantum affine algebras, On a convexity property of tensor products of irreducible, rational representations of $SL(n)$, The Cos\(^\lambda\) and Sin\(^\lambda\) transforms as intertwining operators between generalized principal series representations of SL\((n+1,\mathbb K)\), Nonabelian theta functions of positive genus, A proof of the refined PRV conjecture via the cyclic convolution variety, Borel-de Siebenthal pairs, global Weyl modules and Stanley-Reisner rings, Generalizations of the PRV conjecture. II, Gaussian maps and tensor products of irreducible representations, Orthogonal linear group-subgroup pairs with the same invariants, Standard monomial theoretic proof of prv conjecture, An intrinsic analysis of unitarizable highest weight modules, A refinement of the PRV conjecture, Two generalizations of the PRV conjecture, INTRODUCTION TO YANGIAN SYMMETRY IN INTEGRABLE FIELD THEORY, Modules with a Demazure flag, Ricci-corrected derivatives and invariant differential operators, Positivity of some intersections in \(K_0(G/B)\), Generalized Demazure modules and prime representations in type \(D_n\), A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras, Composantes PRV généralisées et chemins de Littelmann, The ring of sections of a complete symmetric variety.
Cites Work
- Unnamed Item
- Unnamed Item
- Homogeneous vector bundles
- Projective normality of flag varieties and Schubert varieties
- Schubert varieties and Demazure's character formula
- Frobenius splitting and cohomology vanishing for Schubert varieties
- Equations defining Schubert varieties and Frobenius splitting of diagonals
- Demazure character formula in arbitrary Kac-Moody setting
- Vanishing theorems and induced representations
- Lie algebra cohomology and the generalized Borel-Weil theorem
- Representation of complex semi-simple Lie groups and Lie algebras
- On the Demazure character formula
- SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
- A Formula For the Multiplicity of a Weight