Capelli identities for Lie superalgebras
Nazarov, Maxim
Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997), p. 847-872 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@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},
     volume = {30},
     year = {1997},
     pages = {847-872},
     doi = {10.1016/s0012-9593(97)89941-7},
     mrnumber = {99b:17008},
     zbl = {0892.17011},
     mrnumber = {1476298},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1997_4_30_6_847_0}
}

Nazarov, Maxim. Capelli identities for Lie superalgebras. Annales scientifiques de l'École Normale Supérieure, Tome 30 (1997) pp. 847-872. doi : 10.1016/s0012-9593(97)89941-7. http://gdmltest.u-ga.fr/item/ASENS_1997_4_30_6_847_0/

[1] A. Capelli, Sur les opérations dans la théorie des formes algébriques (Math. Ann., Vol. 37, 1890, pp. 1-37). | JFM 22.0137.01

[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 96d:43013 | Zbl 0851.22010

[4] A. Okounkov, Quantum immanants and higher Capelli identities (Transformation Groups, Vol. 1, 1996, pp. 99-126). | MR 97j:17010 | Zbl 0864.17014

[5] M. Nazarov, Yangians and Capelli identities (Amer. Math. Soc. Transl., Vol. 181, 1997, pp. 139-164). | MR 99g:17033 | Zbl 0927.17007

[6] V. Kac, Lie superalgebras (Adv. Math., Vol. 26, 1977, pp. 8-96). | MR 58 #5803 | Zbl 0366.17012

[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 0960.20009

[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 0573.17002

[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 87m:22031 | Zbl 0599.20050

[11] M. Nazarov, Young's symmetrizers for projective representations of the symmetric group (Adv. Math., Vol. 127, 1997, pp. 190-257). | MR 98m:20019 | Zbl 0930.20011

[12] A. Okounkov, Young basis, Wick formula, and higher Capelli identities (Int. Math. Research Notices, 1996, pp. 817-839). | MR 98b:17009 | Zbl 0878.17008

[13] A. Molev, Factorial supersymmetric Schur functions and super Capelli identities, in (“A. A. KIRILLOV Seminar on Representation Theory”, AMS, Providence, 1997). | Zbl 0955.05112

[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 90h:17044 | Zbl 0667.17008

[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 32.0157.02

[16] A. Jucys, Symmetric polynomials and the center of the symmetric group ring (Rep. Math. Phys., Vol. 5, 1974, pp. 107-112). | MR 54 #7597 | Zbl 0288.20014

[17] A. Sergeev, The centre of enveloping algebra of the Lie superalgebra Q(n) (Lett. Math. Phys., Vol. 7, 1983, pp. 177-179). | MR 85i:17004 | Zbl 0539.17003

[18] R. Howe, Remarks on classical invariant theory (Trans. Amer. Math. Soc., Vol. 313, 1989, pp. 539-570). | MR 90h:22015a | Zbl 0674.15021

[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 55 #3013 | Zbl 0346.17011

[20] I. Macdonald, Symmetric functions and Hall polynomials (Clarendon Press, Oxford, 1979). | MR 84g:05003 | Zbl 0487.20007