Capelli identities for Lie superalgebras

Maxim Nazarov

Annales scientifiques de l'École Normale Supérieure (1997)

  • Volume: 30, Issue: 6, page 847-872
  • ISSN: 0012-9593

How to cite

top

Nazarov, Maxim. "Capelli identities for Lie superalgebras." Annales scientifiques de l'École Normale Supérieure 30.6 (1997): 847-872. <http://eudml.org/doc/82452>.

@article{Nazarov1997,
author = {Nazarov, Maxim},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Capelli identities; universal enveloping algebras; simple Lie superalgebras; invariant theory of Lie superalgebras},
language = {eng},
number = {6},
pages = {847-872},
publisher = {Elsevier},
title = {Capelli identities for Lie superalgebras},
url = {http://eudml.org/doc/82452},
volume = {30},
year = {1997},
}

TY - JOUR
AU - Nazarov, Maxim
TI - Capelli identities for Lie superalgebras
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1997
PB - Elsevier
VL - 30
IS - 6
SP - 847
EP - 872
LA - eng
KW - Capelli identities; universal enveloping algebras; simple Lie superalgebras; invariant theory of Lie superalgebras
UR - http://eudml.org/doc/82452
ER -

References

top
  1. [1] A. CAPELLI, Sur les opérations dans la théorie des formes algébriques (Math. Ann., Vol. 37, 1890, pp. 1-37). Zbl22.0137.01JFM22.0137.01
  2. [2] H. WEYL, Classical groups, their invariants and representations (Princeton University Press, Princeton, 1946). Zbl1024.20502
  3. [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). Zbl0851.22010MR96d:43013
  4. [4] A. OKOUNKOV, Quantum immanants and higher Capelli identities (Transformation Groups, Vol. 1, 1996, pp. 99-126). Zbl0864.17014MR97j:17010
  5. [5] M. NAZAROV, Yangians and Capelli identities (Amer. Math. Soc. Transl., Vol. 181, 1997, pp. 139-164). Zbl0927.17007MR99g:17033
  6. [6] V. KAC, Lie superalgebras (Adv. Math., Vol. 26, 1977, pp. 8-96). Zbl0366.17012MR58 #5803
  7. [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). Zbl0960.20009
  8. [8] A. BORODIN and N. ROZHKOVSKAYA, On a superanalogue of the Schur-Weyl duality, Preprint ESI, No. 246, 1995, pp. 1-15). 
  9. [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). Zbl0573.17002
  10. [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). Zbl0599.20050MR87m:22031
  11. [11] M. NAZAROV, Young's symmetrizers for projective representations of the symmetric group (Adv. Math., Vol. 127, 1997, pp. 190-257). Zbl0930.20011MR98m:20019
  12. [12] A. OKOUNKOV, Young basis, Wick formula, and higher Capelli identities (Int. Math. Research Notices, 1996, pp. 817-839). Zbl0878.17008MR98b:17009
  13. [13] A. MOLEV, Factorial supersymmetric Schur functions and super Capelli identities, in (“A. A. KIRILLOV Seminar on Representation Theory”, AMS, Providence, 1997). Zbl0955.05112
  14. [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). Zbl0667.17008MR90h:17044
  15. [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). JFM32.0157.02
  16. [16] A. JUCYS, Symmetric polynomials and the center of the symmetric group ring (Rep. Math. Phys., Vol. 5, 1974, pp. 107-112). Zbl0288.20014MR54 #7597
  17. [17] A. SERGEEV, The centre of enveloping algebra of the Lie superalgebra Q(n) (Lett. Math. Phys., Vol. 7, 1983, pp. 177-179). Zbl0539.17003MR85i:17004
  18. [18] R. HOWE, Remarks on classical invariant theory (Trans. Amer. Math. Soc., Vol. 313, 1989, pp. 539-570). Zbl0674.15021MR90h:22015a
  19. [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). Zbl0346.17011MR55 #3013
  20. [20] I. MACDONALD, Symmetric functions and Hall polynomials (Clarendon Press, Oxford, 1979). Zbl0487.20007MR84g:05003

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.