On q-Deformed gll+1-Whittaker Function II

Communications in Mathematical Physics

Volumn 294, Issue 1, 2009, Pages 121-143

  Gerasimov, Anton ^a,b   Lebedev, Dimitri ^a   Oblezin, Sergey ^a  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b TRINITY COLLEGE DUBLIN   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 72249092732     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-009-0919-9     Document Type: Article

References (28)

1. Atiyah M. F.: K-theory. W. A. Benjamin, New York (1967).
2. Berline N., Getzler E., Vergne M.: Heat Kernels and Dirac Operators. Springer, Berlin-Heidelberg-New York (1992).
3. Braverman, A.: Spaces of Quasi-Maps into the Flag Varieties and their Applications. Proc. ICM 2006, Madrid, Zurich: Eur. Math. Soc., 2006.
4. Braverman A., Finkelberg M.: Finite-difference quantum Toda lattice via equivariant K-theory. Trans. Groups 10, 363-386 (2005).
5. Casselman W., Shalika J.: The unramified principal series of p-adic groups II. The Whittaker function. Comp. Math. 41, 207-231 (1980).
6. Cohen, R. L., Jones, J. D. S., Segal, G. B.: Floer's Infinite Dimensional Morse theory and Homotopy theory. Floer Memorial Volume, Birkhauser Verlag, Prog. in Math. 133, Basel: Birlchäuser, 1995, pp. 287-325.
7. Feigin B., Frenkel E.: Affine Kac-Moody algebras and semi-infinite flag manifolds. Commun. Math. Phys. 128, 161-189 (1990).
8. 3 subspaces and quantum Toda hamiltonians. http://arxiv. org/abs/0707. 1635v2[math. QA], 2007.
9. 1. In: Differential Topology, Infinite-Dimensional Lie Algebras, and Applications. Amer. Math. Soc. Transl. Ser. 2, 194, Providence, RI: Amer. Math. Soc., 1999, pp. 81-112.
10. Feigin, B., Finkelberg, M., Mirković, I.: Semiinfinite Flags. II. Local and Global Intersection Cohomology of Quasimaps' Spaces. In: Differential Topology, Infinite-dimensional Lie Algebras, and Applications. Amer. Math. Soc. Transl. Ser. 2, 194, Providence, RI: Amer. Math. Soc., 1999, pp. 113-148.
11. Gerasimov, A., Kharchev, S., Lebedev, D.: Representation Theory and Quantum Integrability, Progress in Math. 237 Basel: Birlchäuser, 2005, pp. 133-156.
12. Gerasimov, A., Kharchev, S., Lebedev, D., Oblezin, S.: On a Gauss-Givental Representation of Quantum Toda Chain Wave Function. Int. Math. Res. Notices 2006, Aricle ID 96489, 23 pages (2006).
13. l+1-Whittaker Functions I. Commun. Math. Phys., to appear, this issue.
14. l+1-Whittaker Functions III. http://arxiv. org/abs/0805. 3754v2[math. RT], 2008.
15. Gerasimov A., Lebedev D., Oblezin S.: Baxter Q-operators and their arithmetic implications. Lett. Math. Phys. 88(1-3), 3-30 (2009).
16. Gerasimov A., Lebedev D., Oblezin S.: Baxter operator and Archimedean Hecke algebra. Commun. Math. Phys. 284(3), 867-896 (2008).
17. Givental, A.: Homological geometry I. Projective hypersurfaces. Selecta Mathematica, New Series Volume 1, 2 (1995), 325-345.
18. Givental, A.: Stationary phase integrals, quantum toda lattices, flag manifolds and the mirror conjecture. In: Topics in Singularity Theory, Amer. Math. Soc. Transl. Ser., 2 Vol. 180, Providence, RI: Amer. Math. Soc., 1997, pp. 103-115.
19. Givental, A.: A mirror theorem for toric complete intersections. In: Topological Field Theory, Primitive Forms and Related Topics, ed. M. Kashiwara, A. Matsuo, K. Saito, I. Satake, Boston: Birkhäuser, 1998, p. 141.
20. Givental A., Lee Y.-P.: Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups. Invent. Math. 151, 193-219 (2003).
21. Griffiths Ph., Harris J.: Principles of Algebraic Geometry. Wiley-Interscience, New York (1978).
22. Joe, D., Kim, B.: Equivariant mirrors and the Virasoro conjecture for flag manifolds. Int. Math. Res. Notices 2003(15), 859-882, (2003).
23. Kharchev S., Lebedev D., Semenov-Tian-Shansky M.: Unitary representations of uq(sl(2, r)), the modular double and the multiparticle q-deformed Toda chains. Commun. Math. Phys. 225, 573-609 (2002).
24. Kuznetsov A.: Laumon's resolution of Drinfeld's compactification is small. Math. Res. Lett. 4, 349-364 (1997).
25. Laumon G.: Faisceaux automorphes liés aux séries d'Eisenstein. Persp. Math 10, 227-281 (1990).
26. Okonek, Ch., Schneider, M., Spindler, H.: Vector Bundles on Complex Projective Spaces. Progress in Math. 3, Boston, MA: Birkhäuser, 1980.
27. Shintani T.: On an explicit formula for class 1 Whittaker functions on gln over p-adic fields. Proc. Japan Acad. 52, 180-182 (1976).
28. Witten E.: Phases of N = 2 theories in two dimensions. Nucl. Phys. B 403, 159-222 (1993).