Representations of quantum groups and (conditionally) invariant q-difference equations

• Autorzy: Vladimir K. Dobrev
• Języki publikacji: EN

Abstrakty

EN

We give a systematic discussion of the relation between q-difference equations which are conditionally $U_q(𝐺)$-invariant and subsingular vectors of Verma modules over $U_q(𝐺)$ (the Drinfeld-Jimbo q-deformation of a semisimple Lie algebra 𝐺 over ℂg or ℝ). We treat in detail the cases of the conformal algebra, 𝐺 = su(2,2), and its complexification, 𝐺 = sl(4). The conditionally invariant equations are the q-deformed d'Alembert equation and a new equation arising from a subsingular vector proposed by Bernstein-Gel'fand-Gel'fand.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1997
• Tom: 40
• Numer: 1
• Strony: 203-222

Daty

wydano

1997

Twórcy

autor

Vladimir K. Dobrev

• Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria

Bibliografia

• [1] A.O. Barut and R. Rączka, Theory of Group Representations and Applications, II edition, (Polish Sci. Publ., Warsaw, 1980).
• [2] I.N. Bernstein, I.M. Gel'fand and S.I. Gel'fand, Funkts. Anal. Prilozh. 5 (1) (1971) 1; English translation: Funct. Anal. Appl. 5 (1971) 1.
• [3] B. Binegar, C. Fronsdal and W. Heidenreich, J. Math. Phys. 24 (1983) 2828.
• [4] C. De Concini and V.G. Kac, Progress in Math. 92 (Birkhäuser, Boston, 1990) p. 471.
• [5] V.K. Dobrev, J. Math. Phys. 26 (1985) 235.
• [6] V.K. Dobrev, Rep. Math. Phys. 25 (1988) 159.
• [7] V.K. Dobrev, in: Proc. of the International Group Theory Conference (St. Andrews, 1989), eds. C.M. Campbell and E.F. Robertson, Vol. 1, London Math. Soc. Lect. Note Ser. 159 (1991) p. 87.
• [8] V.K. Dobrev, Lett. Math. Phys. 22 (1991) 251.
• [9] V.K. Dobrev, J. Phys. A26 (1993) 1317.
• [10] V.K. Dobrev, J. Phys. A27 (1994) 4841 & 6633, (first as preprint ASI-TPA/10/93 (1993)).
• [11] V.K. Dobrev, Phys. Lett. 341B (1994) 133 & 346B (1995) 427 (first as preprint ASI-TPA/15/94 (June 1994)).
• [12] V.K. Dobrev, preprint ASI-TPA/22/94, (September 1994); invited talk at the Symposium 'Symmetries in Science VIII', (August 1994, Bregenz, Austria), Proceedings, ed. B. Gruber, (Plenum Press, NY, 1995) p. 55.
• [13] V.K. Dobrev, Kazhdan-Lusztig polynomials and subsingular vectors, ICTP preprint IC/96/15 (January 1996).
• [14] V.K. Dobrev and R. Floreanini, J. Phys. A27 (1994) 4831.
• [15] V.G. Drinfeld, Soviet. Math. Dokl. 32 (1985) 2548; in: Proceedings of the International Congress of Mathematicians, Berkeley (1986), Vol. 1 (The American Mathematical Society, Providence, 1987) p. 798.
• [16] P. Furlan, V.B. Petkova and G.M. Sotkov, J. Math. Phys. 28 (1987) 251.
• [17] P. Furlan, V.B. Petkova, G.M. Sotkov and I.T. Todorov, Riv. del Nuovo Cim. 8 No 3 (1985) 1.
• [18] M. Jimbo, Lett. Math. Phys. 10 (1985) 63; Lett. Math. Phys. 11 (1986) 247.
• [19] D. Kazhdan and G. Lusztig, Inv. Math. 53 (1979) 165.
• [20] Abdus Salam and J. Strathdee, Phys. Rev. 184 (1969) 1760.
• [21] G.M. Sotkov and D.Ts. Stoyanov, J. Phys. A13 (1980) 2807; J. Phys. A16 (1983) 2817.
• [22] T. Yao, J. Math. Phys. 8 (1967) 1931; 9 (1968) 1615; 12 (1971) 315.