Noncommutative Schur polynomials and the crystal limit of the Uq Ŝi(2)-vertex model

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 43, 2010, Pages

  Korff, Christian ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78649642157     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/43/434021     Document Type: Article

References (21)

1. Baxter R J 1989 Exactly Solved Models in Statistical Mechanics (London: Academic) (Reprint of the 1982 original, Harcourt Brace Jovanovich Publishers)
2. Beauville A 1996 Conformal blocks, fusion rules and the Verlinde formula Proc. Hirzebruch 65th Conf Algebraic Geometry (Ramat Gan, 1993) (Israel Math. Conf. Proc. vol 9) pp 75-96
3. Bogoliubov N M, Izergin A G and Kitanine N A 1998 Correlation functions for a strongly correlated boson system Nucl. Phys. B 516 501-28
4. Bogoliubov N M, Izergin A G and Korepin V E 1993 Quantum inverse scattering method and correlation functions Cambridge Monographs on Mathematical Physics (Cambridge: Cambridge University Press)
5. Francesco P Di, Mathieu P and Sénéchal D 1997 Conformal field theory Graduate Texts in Contemporary Physics (Berlin: Springer)
6. Chari V and Pressley A 1995 A Guide to Quantum Groups (Cambridge: Cambridge University Press) (Corrected reprint of the 1994 original)
7. Fomin S and Greene C 1998 Noncommutative Schur functions and their applications Discrete Math. 193 179-200 (Selected papers in honour of Adriano Garsia, Taormina, 1994)
8. Fukuda K, Yamada Y and Okado M 2000 Energy functions in box ball systems Int. J. Mod. Phys. A 15 1379-92
9. Fulton W 1997 Young Tableaux (London Mathematical Society Student Texts vol 35) (Cambridge: Cambridge University Press)
10. M automata related to crystals of symmetric tensors J. Math. Phys. 42 274-308
11. Hong J and Kang S-J 2002 Introduction to Quantum Groups and Crystal Bases (Graduate Studies in Mathematics vol 42) (Providence, RI: American Mathematical Society)
12. q (ŝi (n)) at q = 0 Commun. Math. Phys. 136 543-66
13. Kac V G 1985 Infinite-dimensional Lie Algebras 2nd edn (Cambridge: Cambridge University Press)
14. Kac V G and Peterson D H 1984 Infinite-dimensional Lie algebras, theta functions and modular forms Adv. Math. 53 125-264
15. Kashiwara M 1990 Crystalizing the q-analogue of universal enveloping algebras Commun. Math. Phys 133 249-60
16. Korff C and Stroppel C 2010 The ŝi (n) k-WZNW fusion ring: a combinatorial construction and a realisation as quotient of quantum cohomology Adv. Math. at press (doi:10.1016/j.aim.2010.02.021)
17. Lascoux A and Schützenberger M-P 1981 Le monoïde plaxique Noncommutative Structures in Algebra and Geometric Combinatorics (Naples, 1978) (Quad. 'Ricerca Sci.' vol 109) (Rome: CNR) pp 129-56
18. Macdonald I G 1995 Symmetric Functions and Hall Polynomials (Oxford Mathematical Monographs) 2nd edn (Oxford: Clarendon, Oxford University Press)
19. Takahashi D and Satsuma J 1990 A soliton cellular automaton J. Phys. Soc. Japan 59 3514-9
20. Verlinde E 1988 Fusion rules and modular transformations in 2D conformal field theory Nucl. Phys. B 300 360-76
21. Okado M 2007 X = M conjecture Part 3 of Combinatorial Aspect of Integrable Systems ed A Kuniba and M Okado (MSJ Memoirs vol 17) pp 43-73