RUS  ENG
Ïîëíàÿ âåðñèÿ
ÆÓÐÍÀËÛ // Symmetry, Integrability and Geometry: Methods and Applications

SIGMA, 2010, òîì 6, 010, 13 ñòð. (Mi sigma467)

$q$-Analog of Gelfand–Graev Basis for the Noncompact Quantum Algebra $U_q(u(n,1))$
Raisa M. Asherova, Čestmír Burdík, Miloslav Havlíček, Yuri F. Smirnov, Valeriy N. Tolstoy

Ñïèñîê ëèòåðàòóðû

1. Gel'fand I. M., Tsetlin M. L., “Finite-dimensional representations of unimodular matrices group”, Doklady Akad. Nauk SSSR, 71 (1950), 825–828 (in Russian)  mathscinet
2. Nagel J. G., Moshinsky M., “Operators that lower or raise the irreducible vector spaces of $U_{n-1}$ contained in an irreducible vector space of $U_n$”, J. Math. Phys., 6 (1965), 682–694  crossref  mathscinet  zmath  adsnasa
3. Hou P.-Y.,, “Orthonormal bases and infinitesimal operators of the irreducible representations of group $U_n$”, Sci. Sinica, 15 (1966), 763–772  mathscinet  zmath
4. Asherova R. M., Smirnov Yu. F., Tolstoy V. N., “Projection operators for the simple Lie groups. II. General scheme for construction of lowering operators. The case of the group $SU(n)$”, Teoret. Mat. Fiz., 15:1 (1973), 107–119 (in Russian)  mathnet  mathscinet
5. Gelfand I. M., Graev M. I., “Finite-dimensional irreducible representations of unitary and general linear groups and related special functions”, Izv. Akad. Nauk SSSR Ser. Mat., 29:6 (1965), 1329–1356  mathnet  mathscinet; English transl.: Amer. Math. Soc. Transl. (2), 64 (1967), 116–146
6. Barut A., Ra̧czka R., Theory of group representations and applications, Polish Scientific Publishers, Warsaw, 1977  mathscinet
7. Enright T. J., Varadarajan V. S., “On an infinitesimal characterization of the discrete series”, Ann. of Math. (2), 102 (1975), 1–15  crossref  mathscinet  zmath
8. Molev A. I., “Unitarizability of some Enright–Varadarajan $u(p,q)$-modules”, Topics in Representation Theory, Adv. Soviet Math., 2, Amer. Math. Soc., Providence, RI, 1991, 199–219  mathscinet
9. Mickelsson J., “A description of discrete series using step algebra”, Math. Scand., 41 (1977), 63–78  mathscinet  zmath
10. Smirnov Yu. F., Kharitonov Yu. I., “Noncompact quantum algebra $u_q(2,1)$: positive discrete series of irreducible representations”, Proceedings of International Symposium “Symmetries in Science XI” (July 2003, Bregenz, Austria), eds. B. Gruber, G. Marmo and N. Ioshinaga, Kluwer Acad. Publ., Dordrecht, 2004, 505–526  mathscinet  adsnasa; math.QA/0311283
11. Smirnov Yu. F., Kharitonov Yu. I., Asherova R. M., “Noncompact quantum algebra $u_q(2,1)$: intermediate discrete series of unitary irreducible representations”, Phys. Atomic Nuclei, 69 (2006), 1045–1057  crossref  adsnasa  isi
12. Groza V. A., Iorgov N. Z., Klimyk A. U., “Representations of the quantum algebra $U_q(u_{n,1})$”, Algebr. Represent. Theory, 3 (2000), 105–130  crossref  mathscinet  zmath; math.QA/9805032  mathscinet
13. Guizzi V., “A classification of unitary highest weight modules of the quantum analogue of the symmetric pair $(A_n, A_{n-1})$”, J. Algebra, 192 (1997), 102–129  crossref  mathscinet  zmath  isi
14. Tolstoy V. N., “Extremal projectors for quantized Kac–Moody superalgebras and some of their applications”, Quantum Groups (Clausthal, 1989), Lecture Notes in Phys., 370, Springer, Berlin, 1990, 118–125  mathscinet  adsnasa
15. Tolstoy V. N., “Projection operator method for quantum groups”, Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), NATO Sci. Ser. II Math. Phys. Chem., 30, Kluwer Acad. Publ., Dordrecht, 2001, 457–488  mathscinet  zmath; math.QA/0104045
16. Shapovalov N. N., “On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra”, Funct. Anal. Appl., 6 (1972), 307–312  mathnet  crossref  zmath


© ÌÈÀÍ, 2026