Boxed plane partitions as an exactly solvable boson model

Journal of Physics A: Mathematical and General

Volumn 38, Issue 43, 2005, Pages 9415-9430

  Bogoliubov, N M ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 26844499129     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/43/002     Document Type: Article

References (28)

1. Andrews G E 1998 The Theory of Partitions (Cambridge: Cambridge University Press)
2. Vershik A 1996 Statistical mechanics of combinatorial partitions and their limit configurations Funct. Anal. Appl. 30 90
3. Vershik A and Kerov S 1977 Asymptotics of the Plancherel measure of the symmetric group and the limit form of Young tableaux Sov. Math. Dokl. 18 527
4. Cohn H, Larsen M and Propp J 1998 The shape of a typical boxed plane partition New York J. Math. 4 137
5. Destainville N, Mosseri R and Bailly F 1997 Configurational entropy of codimension-one tilings and directed membranes J. Stat. Phys. 87 697
6. Destainville N 1998 Entropy and boundary conditions in random rhombus tilings J. Phys. A: Math. Gen. 31 6123
7. Cohn H, Kenyon R and Propp J 2001 A variational principle for domino tilings J. Am. Math. Soc. 14 297
8. Okounkov A and Reshetikhin N 2003 Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram J. Am. Math. Soc. 16 58
9. Ferrari P L and Spohn H 2003 Step functions for a faceted crystal J. Stat. Phys. 113 1
10. Rajesh R and Dhar D 1998 An exactly solvable anisotropic directed percolation model in three dimensions Phys. Rev. Lett. 81 1646
11. Okounkov A, Reshetikhin N and Vafa C 2003 Quantum Calabi-Yau and classical crystals Preprint hep-th/0309208
12. q(1, 1) J. Phys. A: Math. Gen. 23 L415
13. Faddeev L D, Reshetikhin N Yu and Takhtajan L A 1990 Quantization of Lie groups and Lie algebras Leningr. Math. J. 1 193
14. Carruters P and Nieto M 1968 Phase and angle variables in quantum mechanics Rev. Mod. Phys. 40 411
15. Kashivara M 1990 Crystalizing the q-analogue of universal enveloping algebras Commun. Math. Phys. 133 249
16. Lusztig G 1993 Introduction to quantum groups Progress in Mathematics vol 110 (Basle: Birkhauser)
17. Faddeev L D 1980 Quantum inverse scattering method Sov. Sci. Rev. Math. C 1 107
18. Korepin V E, Bogoliubov N M and Izergin A G 1993 Quantum Inverse Scattering Method and Correlation Functions (Cambridge: Cambridge University Press)
19. Bogoliubov N M, Bullough R K and Timonen J 1994 Critical behavior for correlated strongly coupled boson systems in 1 + 1 dimensions Phys. Rev. Lett. 25 3933
20. Bogoliubov N M and Nassar T 1997 On the spectrum of the non-Hermitian phase-difference model Phys. Lett. A 234 345
21. Bogoliubov N M, Izergin A G and Kitanine N A 1998 Correlation functions for a strongly correlated boson systems Nucl. Phys. B 516 501
22. Bressoud D M 1999 Proofs and Confirmations. The Story of the Alternating Sign Matrix Conjecture (Cambridge: Cambridge University Press)
23. Kulish P P 1981 Quantum difference nonlinear Schrödinger equation Lett. Math. Phys. 5 191
24. Macdonald I G 1995 Symmetric Functions and Hall Polynomials (Oxford: Clarendon)
25. Kuperberg G 1996 Another proof of the alternating-sign matrix conjecture Int. Math. Res. Not. 1996 139
26. Krattenthaller C 1995 The major counting of nonintersecting lattice paths and generating functions of tableaux Mem. Am. Math. Soc. 115 552
27. Izergin A G, Coker D A and Korepin V E 1992 Determinant formula for the six-vertex model J. Phys. A: Math. Gen. 25 4315
28. Izergin A G, Karjalainen E and Kitanine N A 2000 Integrable equations for the partition function of the six-vertex model J. Math. Sci. 100 2141