A commutative algebra on degenerate C P1 and Macdonald polynomials

Journal of Mathematical Physics

Volumn 50, Issue 9, 2009, Pages

  Feigin, B ^a,b,c   Hashizume, K ^d   Hoshino, A ^e   Shiraishi, J ^f   Yanagida, S ^d  

^a LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

^b NATIONAL RESEARCH UNIVERSITY HIGHER SCHOOL OF ECONOMICS   (Russian Federation)

^c INDEPENDENT UNIVERSITY OF MOSCOW   (Russian Federation)

^d KOBE UNIVERSITY   (Japan)

^e SOPHIA UNIVERSITY   (Japan)

^f UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349656663     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3192773     Document Type: Conference Paper

References (27)

1. Arnaudon, D., Buffenoir, E., Ragoucy, E., and Roche, Ph., " Universal solutions of quantum dynamical Yang-Baxter equations.," Lett. Math. Phys. 44, 201 (1998). 10.1023/A:1007498022373
2. N algebras and Macdonald polynomials.," Commun. Math. Phys. 179, 401 (1996). 10.1007/BF02102595
3. Awata, H., Matsuo, Y., Odake, S., and Shiraishi, J., " Collective field theory, Calogero-Sutherland model and generalized matrix model.," Phys. Lett. B 347, 49 (1995). 10.1016/0370-2693(95)00055-P
4. Babelon, O., Bernard, D., and Billey, E., " A quasi-Hopf algebra interpretation of quantum 3j-and 6j -symbols and difference equations.," Phys. Lett. B 375, 89 (1996). 10.1016/0370-2693(96)00225-0
5. Ding, J., and Iohara, K., " Generalization of Drinfeld quantum affine algebras.," Lett. Math. Phys. 41, 183 (1997). 10.1023/A: 1007341410987
6. Drinfeld, V. G., " Quasi-Hopf algebras.," Leningrad Math. J. 1, 1419 (1990).
7. 2) and quasi-Hopf algebras.," Commun. Math. Phys. 195, 651 (1998). 10.1007/s002200050407 (Pubitemid 128114609)
8. Feigin, B., and Frenkel, E., " Quantum W -algebras and elliptic algebras.," Commun. Math. Phys. 178, 653 (1996). 10.1007/BF02108819
9. Feigin, B., and Odesskii, A., " A family of elliptic algebras.," J. Hydraul. Eng. 11, 531 (1997).
10. Feigin, B., and Tsymbaliuk, A., " Heisenberg action in the equivariant K -theory of Hilbert schemes via shuffle algebra.," e-print arXiv:0904.1679.
11. Felder, G., XIth ICMP, Paris, 1994, (International, Cambridge, MA, 1995), pp. 211-218.
12. Frønsdal, C., " Generalization and exact deformations of quantum groups.," Publ. Res. Inst. Math. Sci. 33, 91 (1997). 10.2977/prims/1195145535
13. Frønsdal, C., " Quasi-Hopf deformation of quantum groups.," Lett. Math. Phys. 40, 117 (1997). 10.1023/A:1007379217382
14. Haiman, M., " Macdonald polynomials and geometry.," MSRI Publications 38, 207 (1999).
15. Jing, N. H., " q -Hypergeometric series and Macdonald functions.," J. Algebr. Comb. 3, 291 (1994). 10.1023/A:1022463918288
16. Jimbo, M., Konno, H., Odake, S., and Shiraishi, J., " Quasi-Hopf twistors for elliptic quantum groups.," Transform. Groups 4, 303 (1999). 10.1007/BF01238562
17. 2): Drinfeld currents and vertex operators.," Commun. Math. Phys. 199, 605 (1999). 10.1007/s002200050514
18. Langmann, E., " Second quantization of the elliptic calogero-sutherland model.," Commun. Math. Phys. 247, 321 (2004). 10.1007/s00220-004-1077-8 (Pubitemid 38739953)
19. Langmann, E., " Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model.," J. Math. Phys. 47, 022101 (2006). 10.1063/1.2167807
20. Macdonald, I. G., Oxford Mathematical Monographs, 2nd ed. (Oxford University Press, Oxford, 1995).
21. Odesskii, A. V., " Elliptic algebras.," Russ. Math. Surveys 57, 1127 (2002). 10.1070/RM2002v057n06ABEH000573
22. Noumi, M., private communication (2007).
23. Okounkov, A., and Pandharipande, R., " Quantum cohomology of the Hilbert scheme of points in the plane.," e-print arXiv:math/0411210.
24. Ruijsenaars, S. N. M., " Complete integrability of relativistic Calogero-Moser systems and elliptic function identities.," Commun. Math. Phys. 110, 191 (1987). 10.1007/BF01207363
25. Shiraishi, J., Lectures on Quantum Integrable Systems (SGC Library, Saiensusha, 2003), Vol. 28 (in Japanese).
26. Shiraishi, J., " A family of integral transformations and basic hypergeometric series.," Commun. Math. Phys. 263, 439 (2006). 10.1007/s00220-005-1504-5
27. Shiraishi, J., Kubo, H., Awata, H., and Odake, S., " A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions.," Lett. Math. Phys. 38, 33 (1996). 10.1007/BF00398297