Let G be a connected semisimple algebraic group over , P a parabolic subgroup, and their Lie algebras. We prove a microlocal version of Gyoja's conjectures [2] about a relation between the irreducibility of generalized Verma modules on induced from and the zeroes of b-functions of P-semi-invariants on G. Our method uses a duality for twisted -modules on generalized flag manifolds.
Soient G un groupe algébrique sur connexe semi-simple, P un sous-groupe parabolique, et leurs algèbres de Lie. On démontre une version microlocale des conjectures de Gyoja [2] sur une relation entre l'irreductibilité des modules de Verma généralisés sur induits de et les zéros des b-fonctions des quasi-invariants sur G par rapport à P. Notre méthode utilise une dualité pour les -modules tordus sur les variétés de drapeaux généralisées.
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Corrado Marastoni 1, 2
@article{CRMATH_2002__335_2_111_0, author = {Corrado Marastoni}, title = {Generalized {Verma} modules, \protect\emph{b}-functions of semi-invariants and duality for twisted $ \mathcal{D}$-modules on generalized flag manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {111--116}, publisher = {Elsevier}, volume = {335}, number = {2}, year = {2002}, doi = {10.1016/S1631-073X(02)02449-4}, language = {en}, }
TY - JOUR AU - Corrado Marastoni TI - Generalized Verma modules, b-functions of semi-invariants and duality for twisted $ \mathcal{D}$-modules on generalized flag manifolds JO - Comptes Rendus. Mathématique PY - 2002 SP - 111 EP - 116 VL - 335 IS - 2 PB - Elsevier DO - 10.1016/S1631-073X(02)02449-4 LA - en ID - CRMATH_2002__335_2_111_0 ER -
%0 Journal Article %A Corrado Marastoni %T Generalized Verma modules, b-functions of semi-invariants and duality for twisted $ \mathcal{D}$-modules on generalized flag manifolds %J Comptes Rendus. Mathématique %D 2002 %P 111-116 %V 335 %N 2 %I Elsevier %R 10.1016/S1631-073X(02)02449-4 %G en %F CRMATH_2002__335_2_111_0
Corrado Marastoni. Generalized Verma modules, b-functions of semi-invariants and duality for twisted $ \mathcal{D}$-modules on generalized flag manifolds. Comptes Rendus. Mathématique, Volume 335 (2002) no. 2, pp. 111-116. doi : 10.1016/S1631-073X(02)02449-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02449-4/
[1] Leray's quantization of projective duality, Duke Math. J., Volume 84 (1996) no. 2, pp. 453-496
[2] Highest weight modules and b-functions of semi-invariants, Publ. Res. Inst. Math. Sci., Volume 30 (1994) no. 3, pp. 353-400
[3] b-functions and holonomic systems, Invent. Math., Volume 38 (1976/77), pp. 33-53
[4] The Riemann–Hilbert problem for holonomic systems, Publ. Res. Inst. Math. Sci., Volume 20 (1984) no. 2, pp. 319-365
[5] Representation theory and -modules on flag varieties, Astérisque, Volume 173–174 (1989), pp. 55-109
[6] Grassmann duality for -modules, Ann. Sci. École Norm. Sup., Volume 31 (1998), pp. 459-491
[7] Proximité évanescente II, Compositio Math., Volume 64 (1987), pp. 213-241
[8] Microlocal analysis of prehomogeneous vector spaces, Invent. Math., Volume 62 (1980), pp. 117-179
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