Capelli identities for Lie superalgebras
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 30 (1997) no. 6, pp. 847-872. 
@article{ASENS_1997_4_30_6_847_0,
     author = {Nazarov, Maxim},
     title = {Capelli identities for {Lie} superalgebras},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {847--872},
     publisher = {Elsevier},
     volume = {Ser. 4, 30},
     number = {6},
     year = {1997},
     doi = {10.1016/s0012-9593(97)89941-7},
     zbl = {0892.17011},
     mrnumber = {1476298},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(97)89941-7/}
}
TY  - JOUR
AU  - Nazarov, Maxim
TI  - Capelli identities for Lie superalgebras
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1997
SP  - 847
EP  - 872
VL  - 30
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/s0012-9593(97)89941-7/
DO  - 10.1016/s0012-9593(97)89941-7
LA  - en
ID  - ASENS_1997_4_30_6_847_0
ER  - 
%0 Journal Article
%A Nazarov, Maxim
%T Capelli identities for Lie superalgebras
%J Annales scientifiques de l'École Normale Supérieure
%D 1997
%P 847-872
%V 30
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/s0012-9593(97)89941-7/
%R 10.1016/s0012-9593(97)89941-7
%G en
%F ASENS_1997_4_30_6_847_0
Nazarov, Maxim. Capelli identities for Lie superalgebras. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 30 (1997) no. 6, pp. 847-872. doi : 10.1016/s0012-9593(97)89941-7. http://www.numdam.org/articles/10.1016/s0012-9593(97)89941-7/

[1] A. Capelli, Sur les opérations dans la théorie des formes algébriques (Math. Ann., Vol. 37, 1890, pp. 1-37). | JFM

[2] H. Weyl, Classical groups, their invariants and representations (Princeton University Press, Princeton, 1946).

[3] S. Sahi, The spectrum of certain invariant differential operators associated to a Hermitian symmetric space, in (“Lie Theory and Geometry”, Progress in Math., Vol. 123, Birkhäuser, Boston, 1994, pp. 569-576). | MR | Zbl

[4] A. Okounkov, Quantum immanants and higher Capelli identities (Transformation Groups, Vol. 1, 1996, pp. 99-126). | MR | Zbl

[5] M. Nazarov, Yangians and Capelli identities (Amer. Math. Soc. Transl., Vol. 181, 1997, pp. 139-164). | MR | Zbl

[6] V. Kac, Lie superalgebras (Adv. Math., Vol. 26, 1977, pp. 8-96). | MR | Zbl

[7] V. Ivanov, Dimensions of skew shifted Young diagrams and projective characters of the infinite symmetric group (Zapiski Nauchn. Sem. POMI, Vol. 232, 1997, pp. 116-136 ; English transl. in J. Math. Sciences). | Zbl

[8] A. Borodin and N. Rozhkovskaya, On a superanalogue of the Schur-Weyl duality, Preprint ESI, No. 246, 1995, pp. 1-15).

[9] A. Sergeev, The tensor algebra of the identity representations as a module over the Lie superalgebras GL(n, m) and Q(n) (Math. Sbornik, Vol. 51, 1985, pp. 419-427). | Zbl

[10] I. Cherednik, On special bases of irreducible finite-dimensional representations of the degenerate affine Hecke algebra (Funct. Anal. Appl., Vol. 20, 1986, pp. 87-89). | MR | Zbl

[11] M. Nazarov, Young's symmetrizers for projective representations of the symmetric group (Adv. Math., Vol. 127, 1997, pp. 190-257). | MR | Zbl

[12] A. Okounkov, Young basis, Wick formula, and higher Capelli identities (Int. Math. Research Notices, 1996, pp. 817-839). | MR | Zbl

[13] A. Molev, Factorial supersymmetric Schur functions and super Capelli identities, in (“A. A. KIRILLOV Seminar on Representation Theory”, AMS, Providence, 1997). | Zbl

[14] M. Jimbo, A. Kuniba, T. Miwa and M. Okado, The A(1)n face models (Comm. Math. Phys., Vol. 119, 1988, pp. 543-565). | MR | Zbl

[15] A. Young, On quantitative substitutional analysis I and II (Proc. London Math. Soc., Vol. 33, 1901, pp. 97-146 ; Vol. 34, 1902, pp. 361-397). | JFM

[16] A. Jucys, Symmetric polynomials and the center of the symmetric group ring (Rep. Math. Phys., Vol. 5, 1974, pp. 107-112). | MR | Zbl

[17] A. Sergeev, The centre of enveloping algebra of the Lie superalgebra Q(n) (Lett. Math. Phys., Vol. 7, 1983, pp. 177-179). | MR | Zbl

[18] R. Howe, Remarks on classical invariant theory (Trans. Amer. Math. Soc., Vol. 313, 1989, pp. 539-570). | MR | Zbl

[19] M. Duflo, Sur la classification des idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple (Ann. of Math., Vol. 105, 1977, pp. 107-120). | MR | Zbl

[20] I. Macdonald, Symmetric functions and Hall polynomials (Clarendon Press, Oxford, 1979). | MR | Zbl

Cité par Sources :