On the Demazure character formula
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 18 (1985) no. 3, pp. 389-419.
@article{ASENS_1985_4_18_3_389_0,
     author = {Joseph, A.},
     title = {On the {Demazure} character formula},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {389--419},
     publisher = {Elsevier},
     volume = {Ser. 4, 18},
     number = {3},
     year = {1985},
     doi = {10.24033/asens.1493},
     mrnumber = {87g:17006a},
     zbl = {0589.22014},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/asens.1493/}
}
TY  - JOUR
AU  - Joseph, A.
TI  - On the Demazure character formula
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1985
SP  - 389
EP  - 419
VL  - 18
IS  - 3
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.24033/asens.1493/
DO  - 10.24033/asens.1493
LA  - en
ID  - ASENS_1985_4_18_3_389_0
ER  - 
%0 Journal Article
%A Joseph, A.
%T On the Demazure character formula
%J Annales scientifiques de l'École Normale Supérieure
%D 1985
%P 389-419
%V 18
%N 3
%I Elsevier
%U https://www.numdam.org/articles/10.24033/asens.1493/
%R 10.24033/asens.1493
%G en
%F ASENS_1985_4_18_3_389_0
Joseph, A. On the Demazure character formula. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 18 (1985) no. 3, pp. 389-419. doi : 10.24033/asens.1493. https://www.numdam.org/articles/10.24033/asens.1493/

[1] M. Demazure, Désingularisation des variétés de Schubert généralisées (Ann. scient. Éc. Norm. sup., T. 6, Sect. 2, 1974, pp. 53-88). | Numdam | MR | Zbl

[2] M. Demazure, Une nouvelle formule des caractères (Bull. Sci. Math., T. 98, 1974, pp. 163-172). | MR | Zbl

[3] J. Dixmier, Algèbres enveloppantes (cahiers scientifique Vol. XXXVII, Gauthier-Villars, Paris, 1973). | MR | Zbl

[4] A. Joseph, On the Variety of a Highest Weight Module (J. Algebra). | MR | Zbl

[5] A. Joseph, Completion Functors in the O Category in Lecture notes in mathematics, No. 1020, Springer-Verlag, Berlin/Heidelberg/New York, 1983. | MR | Zbl

[6] A. Joseph, Application de la théorie des anneaux aux algèbres enveloppantes, mimeographed notes, Paris 1981.

[7] A. Joseph, The Enright Functor on the Bernstein-Gelfand-Gelfand Category O (Invent. Math., Vol. 67, 1982, pp. 423-445). | MR | Zbl

[8] M. Demazure, A Very Simple Proof of Bott's Theorem (Invent. Math., Vol. 33 1976, pp. 271-272). | MR | Zbl

[9] A. Joseph, Goldie Rank in the Enveloping Algebra of a Semisimple Lie Algebra, III (J. Alg., Vol. 73, 1981, pp. 295-326). | MR | Zbl

[10] O. Gabber and A. Joseph, Towards the Kazhdan-Lusztig Conjecture (Ann. scient. Ec. Norm. Sup., T. 14, 1981, pp. 261-302). | Numdam | MR | Zbl

[11] I. N. Bernstein, I. M. Gelfand and S. I. Gelfand, Schubert Cells and Cohomology of the Spaces G/P (Uspekhi Matemat. Nauk ; Vol. 28, 1973, pp. 3-26 ; Eng. transl. Russian mathematical Surveys, Vol. 28, 1973, pp. 3-26). | MR | Zbl

[12] B. Kostant, Lie Algebra Cohomology and the Generalized Borel-Weil Theorem (Ann. Math., Vol. 74, 1961, pp. 329-387). | MR | Zbl

[13] J.-L. Verdier, Categories derivées, In SGA 41/2, Cohomologie Etale, LN 569, Springer-Verlag, Berlin/Heidelberg/New York, 1977. | MR | Zbl

[14] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Adison-Wesley, London, 1969. | MR | Zbl

  • Gao, Yibo; Hodges, Reuven; Yong, Alexander Levi-spherical Schubert varieties, Advances in Mathematics, Volume 439 (2024), p. 109486 | DOI:10.1016/j.aim.2024.109486
  • Assaf, Sami; Dranowski, Anne; González, Nicolle Extremal Tensor Products of Demazure Crystals, Algebras and Representation Theory, Volume 27 (2024) no. 1, p. 627 | DOI:10.1007/s10468-023-10231-z
  • Kus, Deniz; Venkatesh, Rajendran Simplified presentations and embeddings of Demazure modules, Israel Journal of Mathematics, Volume 263 (2024) no. 1, p. 475 | DOI:10.1007/s11856-024-2652-7
  • Dumanski, Ilya; Feigin, Evgeny Reduced arc schemes for Veronese embeddings and global Demazure modules, Communications in Contemporary Mathematics, Volume 25 (2023) no. 08 | DOI:10.1142/s0219199722500341
  • Chihara, Masahiro Demazure Slices of Type A2l(2), Algebras and Representation Theory, Volume 25 (2022) no. 2, p. 491 | DOI:10.1007/s10468-021-10032-2
  • Brito, Matheus; Chari, Vyjayanthi; Kus, Deniz; Venkatesh, R. Quantum Affine Algebras, Graded Limits and Flags, Journal of the Indian Institute of Science, Volume 102 (2022) no. 3, p. 1001 | DOI:10.1007/s41745-022-00308-x
  • Chirivì, Rocco; Fang, Xin; Littelmann, Peter Seshadri stratification for Schubert varieties and standard monomial theory, Proceedings - Mathematical Sciences, Volume 132 (2022) no. 2 | DOI:10.1007/s12044-022-00707-1
  • Kushwaha, Mrigendra Singh; Raghavan, K.N.; Viswanath, Sankaran A study of Kostant-Kumar modules via Littelmann paths, Advances in Mathematics, Volume 381 (2021), p. 107614 | DOI:10.1016/j.aim.2021.107614
  • Kato, Syu Frobenius splitting of Schubert varieties of semi-infinite flag manifolds, Forum of Mathematics, Pi, Volume 9 (2021) | DOI:10.1017/fmp.2021.5
  • Dumanski, Ilya; Feigin, Evgeny; Finkelberg, Michael Beilinson–Drinfeld Schubert varieties and global Demazure modules, Forum of Mathematics, Sigma, Volume 9 (2021) | DOI:10.1017/fms.2021.36
  • Rasmussen, Jørgen; Walton, Mark A. Demazure formula for A n Weyl polytope sums, Journal of Mathematical Physics, Volume 62 (2021) no. 10 | DOI:10.1063/5.0058465
  • Walton, Mark A. Demazure Formulas for Weight Polytopes, Quantum Theory and Symmetries (2021), p. 287 | DOI:10.1007/978-3-030-55777-5_27
  • Cherednik, Ivan; Kato, Syu Nonsymmetric Rogers-Ramanujan sums and thick Demazure modules, Advances in Mathematics, Volume 374 (2020), p. 107335 | DOI:10.1016/j.aim.2020.107335
  • Feigin, Evgeny; Kato, Syu; Makedonskyi, Ievgen Representation theoretic realization of non-symmetric Macdonald polynomials at infinity, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2020 (2020) no. 764, p. 181 | DOI:10.1515/crelle-2019-0011
  • Feigin, E. B. PBW Degeneration: Algebra, Geometry, and Combinatorics, Journal of Mathematical Sciences, Volume 235 (2018) no. 6, p. 685 | DOI:10.1007/s10958-018-4089-1
  • Brito, Matheus; Chari, Vyjayanthi; Moura, Adriano DEMAZURE MODULES OF LEVEL TWO AND PRIME REPRESENTATIONS OF QUANTUM AFFINE, Journal of the Institute of Mathematics of Jussieu, Volume 17 (2018) no. 1, p. 75 | DOI:10.1017/s1474748015000407
  • Kato, Syu Demazure character formula for semi-infinite flag varieties, Mathematische Annalen, Volume 371 (2018) no. 3-4, p. 1769 | DOI:10.1007/s00208-018-1652-5
  • Feigin, Evgeny; Makedonskyi, Ievgen Generalized Weyl modules, alcove paths and Macdonald polynomials, Selecta Mathematica, Volume 23 (2017) no. 4, p. 2863 | DOI:10.1007/s00029-017-0346-2
  • Watanabe, Masaki An approach towards Schubert positivities of polynomials using Kraśkiewicz–Pragacz modules, European Journal of Combinatorics, Volume 58 (2016), p. 17 | DOI:10.1016/j.ejc.2016.04.010
  • Fourier, Ghislain PBW-degenerated Demazure modules and Schubert varieties for triangular elements, Journal of Combinatorial Theory, Series A, Volume 139 (2016), p. 132 | DOI:10.1016/j.jcta.2015.12.001
  • Kus, Deniz; Venkatesh, R. Twisted Demazure modules, fusion product decomposition and twisted 𝑄-systems, Representation Theory of the American Mathematical Society, Volume 20 (2016) no. 4, p. 94 | DOI:10.1090/ert/478
  • Venkatesh, R. Fusion Product Structure of Demazure Modules, Algebras and Representation Theory, Volume 18 (2015) no. 2, p. 307 | DOI:10.1007/s10468-014-9495-6
  • Azenhas, O.; Emami, A. An analogue of the Robinson–Schensted–Knuth correspondence and non-symmetric Cauchy kernels for truncated staircases, European Journal of Combinatorics, Volume 46 (2015), p. 16 | DOI:10.1016/j.ejc.2014.11.006
  • Chari, Vyjayanthi; Ion, Bogdan; Kus, Deniz Weyl Modules for the Hyperspecial Current Algebra, International Mathematics Research Notices, Volume 2015 (2015) no. 15, p. 6470 | DOI:10.1093/imrn/rnu135
  • Naoi, Katsuyuki Demazure modules and graded limits of minimal affinizations, Representation Theory of the American Mathematical Society, Volume 17 (2013) no. 18, p. 524 | DOI:10.1090/s1088-4165-2013-00442-9
  • Naoi, Katsuyuki Weyl modules, Demazure modules and finite crystals for non-simply laced type, Advances in Mathematics, Volume 229 (2012) no. 2, p. 875 | DOI:10.1016/j.aim.2011.10.005
  • Naoi, Katsuyuki Fusion products of Kirillov–Reshetikhin modules and the X=M conjecture, Advances in Mathematics, Volume 231 (2012) no. 3-4, p. 1546 | DOI:10.1016/j.aim.2012.07.003
  • Joseph, Anthony Consequences of the Littelmann Path Theory for the Structure of the Kashiwara B(∞) Crystal, Highlights in Lie Algebraic Methods, Volume 295 (2012), p. 25 | DOI:10.1007/978-0-8176-8274-3_2
  • Montagard, P. L.; Pasquier, B.; Ressayre, N. Two generalizations of the PRV conjecture, Compositio Mathematica, Volume 147 (2011) no. 4, p. 1321 | DOI:10.1112/s0010437x10005233
  • Mason, S. An explicit construction of type A Demazure atoms, Journal of Algebraic Combinatorics, Volume 29 (2009) no. 3, p. 295 | DOI:10.1007/s10801-008-0133-4
  • Fourier, G.; Littelmann, P. Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions, Advances in Mathematics, Volume 211 (2007) no. 2, p. 566 | DOI:10.1016/j.aim.2006.09.002
  • Kannan, S. Senthamarai Cohomology of line bundles on Schubert varieties in the Kac–Moody setting, Journal of Algebra, Volume 310 (2007) no. 1, p. 88 | DOI:10.1016/j.jalgebra.2006.10.020
  • Joseph, Anthony Modules with a Demazure flag, Studies in Lie Theory, Volume 243 (2006), p. 131 | DOI:10.1007/0-8176-4478-4_8
  • Mathieu, Olivier Positivity of some intersections in K0(G/B), Journal of Pure and Applied Algebra, Volume 152 (2000) no. 1-3, p. 231 | DOI:10.1016/s0022-4049(99)00139-5
  • Kumar, Shrawan The nil Hecke ring and singularity of Schubert varieties, Inventiones Mathematicae, Volume 123 (1996) no. 1, p. 471 | DOI:10.1007/bf01232388
  • Kumar, Shrawan The nil Hecke ring and singularity of Schubert varieties, Inventiones mathematicae, Volume 123 (1996) no. 3, p. 471 | DOI:10.1007/s002220050038
  • Cox, Ben 𝔉-categories and 𝔉-functors in the representation theory of Lie algebras, Transactions of the American Mathematical Society, Volume 343 (1994) no. 1, p. 433 | DOI:10.1090/s0002-9947-1994-1191610-7
  • Cohen, Arjeh M. Coxeter Groups and three Related Topics, Generators and Relations in Groups and Geometries (1991), p. 235 | DOI:10.1007/978-94-011-3382-1_9
  • Andersen, Henning Haahr; Polo, Patrick; Kexin, Wen Representations of quantum algebras, Inventiones mathematicae, Volume 104 (1991) no. 1, p. 1 | DOI:10.1007/bf01245066
  • Mathieu, Olivier Filtrations of B-modules, Duke Mathematical Journal, Volume 59 (1989) no. 2 | DOI:10.1215/s0012-7094-89-05919-x
  • Hall, Mark E. An introduction to schubert submodules, Lie Algebras, Madison 1987, Volume 1373 (1989), p. 111 | DOI:10.1007/bfb0088891
  • van der Kallen, Wilberd Longest weight vectors and excellent filtrations, Mathematische Zeitschrift, Volume 201 (1989) no. 1, p. 19 | DOI:10.1007/bf01161991
  • Kumar, Shrawan Demazure character formula in arbitrary Kac-Moody setting, Inventiones Mathematicae, Volume 89 (1987) no. 2, p. 395 | DOI:10.1007/bf01389086
  • Thomason, R. W. Lefschetz-Riemann-Roch theorem and coherent trace formula, Inventiones Mathematicae, Volume 85 (1986) no. 3, p. 515 | DOI:10.1007/bf01390328

Cité par 44 documents. Sources : Crossref