Hypergeometric Functions Related to Schur $Q$-Polynomials and the $B$KP Equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 2, pp. 253-270
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce hypergeometric functions related to projective Schur functions $Q_{\lambda}$ and describe their properties. Linear equations, integral representations, and Pfaffian representations are obtained. These hypergeometric functions are vacuum expectations of free fermion fields and are therefore tau functions of the so-called $B$KP hierarchy of integrable equations.
Keywords: projective Schur functions, hypergeometric functions, soliton theory.
@article{TMF_2003_137_2_a10,
     author = {A. Yu. Orlov},
     title = {Hypergeometric {Functions} {Related} to {Schur} $Q${-Polynomials} and the $B${KP} {Equation}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {253--270},
     year = {2003},
     volume = {137},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a10/}
}
TY  - JOUR
AU  - A. Yu. Orlov
TI  - Hypergeometric Functions Related to Schur $Q$-Polynomials and the $B$KP Equation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2003
SP  - 253
EP  - 270
VL  - 137
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a10/
LA  - ru
ID  - TMF_2003_137_2_a10
ER  - 
%0 Journal Article
%A A. Yu. Orlov
%T Hypergeometric Functions Related to Schur $Q$-Polynomials and the $B$KP Equation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2003
%P 253-270
%V 137
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a10/
%G ru
%F TMF_2003_137_2_a10
A. Yu. Orlov. Hypergeometric Functions Related to Schur $Q$-Polynomials and the $B$KP Equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 2, pp. 253-270. http://geodesic.mathdoc.fr/item/TMF_2003_137_2_a10/

[1] E. Date, M. Jimbo, M. Kashiwara, T. Miwa, “Transformation groups for soliton equations”, Nonlinear Integrable Systems: Classical Theory and Quantum Theory, Proc. of RIMS Symp. (Kyoto, Japan, 13–16 May, 1981), eds. M. Jimbo, T. Miwa, World Scientific, Singapore, 1983, 39–120 | MR

[2] E. Date, M. Jimbo, M. Kashiwara, T. Miwa, Phys. D, 4 (1982), 343–365 | DOI | MR | Zbl

[3] V. E. Zakharov, A. B. Shabat, Funkts. analiz i ego prilozh., 3:3 (1974), 43–53 | Zbl

[4] Y. You, “Polynomial solutions of the BKP hierarchy and projective representations of symmetric groups”, Infinite-Dimensional Lie Algebras and Groups, Adv. Ser. Math. Phys., 7, ed. V. G. Kac, World Scientific, Teaneck, NJ, 1989, 449–464 | MR

[5] J. J. C. Nimmo, J. Phys. A, 23 (1990), 751–760 | DOI | MR | Zbl

[6] I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon, Oxford, 1995 | MR | Zbl

[7] A. Yu. Orlov, D. M. Scherbin, Phys. D, 152–153 (2001), 51–65 ; E-print math-ph/0003011 | DOI | MR | Zbl

[8] A. Yu. Orlov, D. Scherbin, J. Phys. A, 34 (2001), 2295–2310 | DOI | MR | Zbl

[9] V. G. Kac, J. van de Leur, “The geometry of spinors and the multicomponent BKP and DKP hierarchies”, The Bispectral Problem, Proc. of the CRM Workshop (Montréal, Canada, March 1997), CMR Proc. Lect. Notes, 14, eds. J. Harnad, A. Kasman, AMS, Providence, RI, 1998, 159–202 | DOI | MR

[10] I. Schur, J. Reine Angew. Math., 139 (1911), 155–250 | MR | Zbl

[11] A. Yu. Orlov, “Vertex operators, $\partial$ bar problem, symmetries, Hamiltonian and Lagrangian formalism of (2+1) dimensional integrable systems”, Plasma Theory and Nonlinear and Turbulent Processes in Physics, Proc. 3rd Intl. Workshop. V. 1 (1987), eds. V. G. Baryakhtar et al., World Scientific, Singapore, 1988, 116–134 | MR | Zbl

[12] C. A. Tracy, H. Widom, A limit theorem for shifted Schur measures, E-print math.PR/0210255 | MR

[13] A. Yu. Orlov, D. M. Scherbin, Fermionic representation for basic hypergeometric functions related to Schur polynomials, E-print nlin.SI/0001001

[14] J. Harnad, A. Yu. Orlov, “Matrix integrals as Borel sums of Schur function expansions”, Symmetry and Perturbation Theory, Proc. Intl. Conf. (SPT 2002), eds. S. Abenda, G. Gaeta, S. Walcher, World Scientific, Singapore, 2003 ; E-print nlin.SI/0209035 | MR

[15] P. van Moerbeke, “Integrable lattices: Random matrices and random permutations”, Random Matrices and Their Applications, MSRI Publ., 40, eds. P. Bleher, A. Its, Cambridge Univ. Press, New York, 2001 ; E-print math.CO/0010135 | MR

[16] I. K. Kostov, Nucl. Phys. Proc. Suppl. A, 45 (1996), 13–28 ; E-print hep-th/9509124 | DOI | MR

[17] I. Loutsenko, V. Spiridonov, Nucl. Phys. B, 538 (1998), 731–751 ; E-print solv-int/9909022 | DOI | MR