Nous étudions les polynômes de Hilbert–Poincaré pour les modules PBW-gradués associés aux modules simples d'une algèbre de Lie simple complexe. Le calcul de leur degré peut être restreint aux modules de plus haut poids fondamental. Nous donnons une formule explicite pour ces degrés.
In this note, we study the Hilbert–Poincaré polynomials for the associated PBW-graded modules of simple modules for a simple complex Lie algebra. The computation of their degree can be reduced to modules of fundamental highest weight. We provide these degrees explicitly.
Accepté le :
Publié le :
@article{CRMATH_2014__352_12_959_0, author = {Backhaus, Teodor and Bossinger, Lara and Desczyk, Christian and Fourier, Ghislain}, title = {The degree of the {Hilbert{\textendash}Poincar\'e} polynomial of {PBW-graded} modules}, journal = {Comptes Rendus. Math\'ematique}, pages = {959--963}, publisher = {Elsevier}, volume = {352}, number = {12}, year = {2014}, doi = {10.1016/j.crma.2014.09.027}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2014.09.027/} }
TY - JOUR AU - Backhaus, Teodor AU - Bossinger, Lara AU - Desczyk, Christian AU - Fourier, Ghislain TI - The degree of the Hilbert–Poincaré polynomial of PBW-graded modules JO - Comptes Rendus. Mathématique PY - 2014 SP - 959 EP - 963 VL - 352 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.09.027/ DO - 10.1016/j.crma.2014.09.027 LA - en ID - CRMATH_2014__352_12_959_0 ER -
%0 Journal Article %A Backhaus, Teodor %A Bossinger, Lara %A Desczyk, Christian %A Fourier, Ghislain %T The degree of the Hilbert–Poincaré polynomial of PBW-graded modules %J Comptes Rendus. Mathématique %D 2014 %P 959-963 %V 352 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.09.027/ %R 10.1016/j.crma.2014.09.027 %G en %F CRMATH_2014__352_12_959_0
Backhaus, Teodor; Bossinger, Lara; Desczyk, Christian; Fourier, Ghislain. The degree of the Hilbert–Poincaré polynomial of PBW-graded modules. Comptes Rendus. Mathématique, Tome 352 (2014) no. 12, pp. 959-963. doi : 10.1016/j.crma.2014.09.027. http://www.numdam.org/articles/10.1016/j.crma.2014.09.027/
[1] PBW filtration: Feigin–Fourier–Littelmann modules via Hasse diagrams, 2014 | arXiv
[2] Minuscule Schubert varieties: poset polytopes, PBW-degenerated Demazure modules, and Kogan faces, 2014 (Preprint) | arXiv
[3] Degenerate flag varieties of type A and C are Schubert varieties, 2014 (Preprint) | arXiv
[4] G. Cerulli Irelli, M. Lanini, P. Littelmann, Degenerate flag varieties and Schubert varieties, Preprint, 2014.
[5] Extremal part of the PBW-filtration and E-polynomials, 2013 (Preprint) | arXiv
[6] degeneration of flag varieties, Sel. Math. New Ser., Volume 18 (2012) no. 3, pp. 513-537
[7] Nonsymmetric Macdonald polynomials, Demazure modules and PBW filtration, 2014 (Preprint) | arXiv
[8] PBW filtration and bases for irreducible modules in type , Transform. Groups, Volume 16 (2011) no. 1, pp. 71-89
[9] PBW filtration and bases for symplectic Lie algebras, Int. Math. Res. Not., Volume 1 (2011) no. 24, pp. 5760-5784
[10] Favourable modules: filtrations, polytopes, Newton–Okounkov bodies and flat degenerations, 2013 | arXiv
[11] PBW-filtration over and compatible bases for in type and , Springer Proc. Math. Stat., Volume 40 (2013), pp. 35-63
[12] New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules, 2014 (Preprint) | arXiv
[13] PBW-degenerated Demazure modules and Schubert varieties for triangular elements, 2014 | arXiv
[14] Essential signatures and canonical bases in irreducible representations of the group , 2011 (Diploma thesis)
[15] Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, vol. 9, Springer-Verlag, New York, 1972
[16] A formula for the multiplicity of a weight, Trans. Amer. Math. Soc., Volume 93 (1959), pp. 53-73
Cité par Sources :