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Cayley-Hamilton theorem for quantum matrix algebras of $GL(m\vert n)$ type

Author(s): D. I. Gurevich; P. N. Pyatov; P. A. Saponov
Translated by: the authors
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 1.
Journal: St. Petersburg Math. J. 17 (2006), 119-135.
MSC (2000): Primary 81R05
Posted: January 19, 2006
MathSciNet review: 2140677
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of $GL(m\vert n)$ type.

References:

[DKS]: E. V. Damaskinskii, P. P. Kulish, and M. A. Sokolov, Gauss decomposition of quantum groups and supergroups, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 224 (1995), 155-177; English transl., J. Math. Sci. (New York) 88 (1998), no. 2, 208-223. MR 1364848 (97g:17009)
[DJ1]: R. Dipper and G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. (3) 52 (1986), 20-52. MR 0812444 (88b:20065)
[DJ2]: -, Blocks and idempotents of Hecke algebras of general linear groups, Proc. London Math. Soc. (3) 54 (1987), 57-82. MR 0872250 (88m:20084)
[D]: V. G. Drinfel'd, Quasi-Hopf algebras, Algebra i Analiz 1 (1989), no. 6, 114-148; English transl., Leningrad Math. J. 1 (1990), no. 6, 1419-1457. MR 1047964 (91b:17016)
[FP]: L. D. Faddeev and P. N. Pyatov, The differential calculus on quantum linear groups, Contemporary Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, vol. 175, Amer. Math. Soc., Providence, RI, 1996, pp. 35-47. MR 1402914 (97j:81139)
[FRT]: N. Yu. Reshetikhin, L. A. Takhtadzhyan, and L. D. Faddeev, Quantization of Lie groups and Lie algebras, Algebra i Analiz 1 (1989), no. 1, 178-206; English transl., Leningrad Math. J. 1 (1990), no. 1, 193-225. MR 1015339 (90j:17039)
[G]: D. I. Gurevich, Algebraic aspects of the quantum Yang-Baxter equation, Algebra i Analiz 2 (1990), no. 4, 119-148; English transl., Leningrad Math. J. 2 (1991), no. 4, 801-828. MR 1080202 (93e:17018)
[Gou]: M. D. Gould, On the matrix elements of the generators, J. Math. Phys. 22 (1981), 15-22. MR 0604445 (82a:17005)
[GPS]: D. Gurevich, P. Pyatov, and P. Saponov, Hecke symmetries and characteristic relations on reflection equation algebras, Lett. Math. Phys. 41 (1997), 255-264. MR 1463875 (98g:81078)
[GS]: D. Gurevich and P. Saponov, Quantum line bundles via Cayley-Hamilton identity, J. Phys. A 34 (2001), no. 21, 4553-4569. MR 1835952 (2002e:17020)
[GS2]: -, Quantum line bundles on a noncommutative sphere, J. Phys. A 35 (2002), 9629-9643. MR 1946944 (2003k:17020)
[Isa]: A. P. Isaev, Quantum groups and Yang-Baxter equations, Fiz. Èlementar. Chastits i Atom. Yadra 26 (1995), 1204-1263; English transl., Phys. Particles Nuclei 26 (1995), 501-526.
[IOP1]: A. P. Isaev, O. V. Ogievetsky, and P. N. Pyatov, On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities, J. Phys. A 32 (1999), L115-L121. MR 1678401 (2000c:81131)
[IOP2]: -, Cayley-Hamilton-Newton identities and quasitriangular Hopf algebras, Supersymmetries and Quantum Symmetries (Dubna, July 27-31, 1999) (E. Ivanov, S. Krivonos, and A. Pashnev, eds.), JINR, Dubna, E2-2000-82, pp. 397-405 (English); Preprint math.QA/9912197
[IOPS]: A. P. Isaev, O. Ogievetsky, P. N. Pyatov, and P. A. Saponov, Characteristic polynomials for quantum matrices, Supersymmetries and Quantum Symmetries (Dubna, Russia, 1997) (J. Wess and E. Ivanov, eds.), Lecture Notes in Phys., vol. 524, Springer-Verlag, Berlin, 1999, pp. 322-330. MR 1743219 (2000m:81084)
[IP]: A. P. Isaev and P. N. Pyatov, Covariant differential complexes on quantum linear groups, J. Phys. A 28 (1995), 2227-2246. MR 1338072 (96g:81120)
[KT1]: I. Kantor and I. Trishin, On a concept of determinant in the supercase, Comm. Algebra 22 (1994), 3679-3739. MR 1280094 (95c:15062)
[KT2]: -, On the Cayley-Hamilton equation in the supercase, Comm. Algebra 27 (1999), 233-259. MR 1668248 (2000a:16083a)
[KS]: P. P. Kulish and R. Sasaki, Covariance properties of reflection equation algebras, Prog. Theoret. Phys. 89 (1993), 741-761. MR 1215910 (94e:16045)
[Mac]: I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd ed., Oxford Math. Monogr., Oxford Univ. Press, New York, 1995. MR 1354144 (96h:05207)
[M1]: G. E. Murphy, On the representation theory of the symmetric groups and associated Hecke algebras, J. Algebra 152 (1992), 492-513. MR 1194316 (94c:17031)
[M2]: -, The representations of Hecke algebras of type , J. Algebra 173 (1995), 97-121. MR 1327362 (96b:20013)
[NT]: M. Nazarov and V. Tarasov, Yangians and Gelfand-Zetlin bases, Publ. Res. Inst. Math. Sci. 30 (1994), 459-478. MR 1299525 (96m:17033)
[OP]: O. Ogievetsky and P. Pyatov, Lecture on Hecke algebras, Symmetries and Integrable Systems (Dubna, Russia, June 8-11, 1999), JINR, Dubna, D2,5-2000, 218, pp. 39-88 (English); Preprint CPT-2000/P. 4076 and MPI 01-40.
[OP2 ]: -, Cayley-Hamilton identities for quantum matrix algebras of Birman-Murakami-Wenzl type (in preparation).
[PS]: P. Pyatov and P. Saponov, Characteristic relations for quantum matrices, J. Phys. A 28 (1995), 4415-4421. MR 1351938 (97b:81051)
[R]: Ram A., Seminormal representations of Weyl groups and Iwahori-Hecke algebras, Proc. London Math. Soc. (3) 75 (1997), 99-133, [arXiv:math.RT/9511223]. MR 1444315 (98d:20007)

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