Analogues of Kostant's ...-cohomology formulas for unitary highest weight modules.
Thomas J. Enright (1988)
Journal für die reine und angewandte Mathematik
Humphreys, J.E. (2002)
Experimental Mathematics
Anthony Joseph (1992)
Annales scientifiques de l'École Normale Supérieure
Vyjayanthi Chari (1985)
Inventiones mathematicae
Olivier Mathieu (1990/1991)
Séminaire Bourbaki
Walter Borho (1977)
Mathematische Annalen
Shrawan Kumar (1990)
Mathematische Annalen
Svatopluk Krýsl (2004)
Acta Universitatis Carolinae. Mathematica et Physica
Michael Falk, Vadim Schechtman, Alexander Varchenko (2014)
Journal de l’École polytechnique — Mathématiques
We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik–Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.
R. Aminou, Y. Kosmann-Schwarzbach (1988)
Annales de l'I.H.P. Physique théorique
Stefano Capparelli (2003)
Bollettino dell'Unione Matematica Italiana
Forniamo un calcolo esplicito della funzione di partizione di Kostant per algebre di Lie complesse di rango . La tecnica principale consiste nella riduzione a casi più semplici ed all'uso di funzioni generatrici.
Roman Lávička (2010)
Archivum Mathematicum
Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as -modules. As finite-dimensional irreducible -modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these orthogonal bases form the Appell system and coincide with those constructed recently by S. Bock and K. Gürlebeck in [3]. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.
Tonny A. Springer (1974/1975)
Séminaire Dubreil. Algèbre et théorie des nombres
B. Cox, V. Futorny, D. Melville (1996)
Mathematische Zeitschrift
Henning Haahr Andersen, Volodymyr Mazorchuk (2015)
Journal of the European Mathematical Society
In this paper we study the BGG-categories associated to quantum groups. We prove that many properties of the ordinary BGG-category for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for and for finite dimensional -modules we are able to determine...
Jacques Dixmier (1972/1973)
Séminaire Bourbaki
Serganova, Vera (1998)
Documenta Mathematica
N.R. Wallach, Rocha-Caridi, A. (1983)
Inventiones mathematicae
Nolan R. Wallach, Alvany Rocha-Caridi (1984)
Mathematische Zeitschrift
Patureau-Mirand, Bertrand (2002)
Geometry & Topology