Cylindric skew Schur functions

Advances in Mathematics

Volumn 205, Issue 1, 2006, Pages 275-312

  McNamara, Peter ^a  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

Author keywords

Cylindric Schur function; Cylindric skew Schur function; Gromov Witten invariant; P partition; Schur function; Schur positivity; Skew Schur function

Indexed keywords

EID: 33746886310     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2005.07.011     Document Type: Article

References (24)

1. Bender E.A., and Knuth D.E. Enumeration of plane partitions. J. Combin. Theory Ser. A 13 (1972) 40-54
2. Bertram A., Ciocan-Fontanine I., and Fulton W. Quantum multiplication of Schur polynomials. J. Algebra 219 2 (1999) 728-746
3. A.S. Buch, Littlewood-Richardson calculator, 1999, available from 〈http://home.imf.au.dk/abuch/lrcalc/〉.
4. Cummins C.J. su (n) and sp (2 n) WZW fusion rules. J. Phys. A 24 2 (1991) 391-400
5. L. Geissinger, Hopf algebras of symmetric functions and class functions, in: Combinatoire et représentation du groupe symétrique (Actes Table Ronde C.N.R.S., Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976), Lecture Notes in Mathematics, vol. 579, Springer, Berlin, 1977, pp. 168-181.
6. I.M. Gessel, Multipartite P-partitions and inner products of skew Schur functions, in: Combinatorics and Algebra (Boulder, Colo., 1983), Contemporary Mathematics, vol. 34, American Mathematical Society, Providence, RI, 1984, pp. 289-317.
7. Gessel I.M., and Krattenthaler C. Cylindric partitions. Trans. Amer. Math. Soc. 349 2 (1997) 429-479
8. Goodman F.M., and Wenzl H. Littlewood-Richardson coefficients for Hecke algebras at roots of unity. Adv. in Math. 82 2 (1990) 244-265
9. Kac V.G. Infinite-dimensional Lie Algebras. third ed. (1990), Cambridge University Press, Cambridge
10. Macdonald I.G. Symmetric functions and Hall polynomials, Oxford Mathematical Monographs. second ed. (1995), Clarendon Press, Oxford University Press, New York
11. Malvenuto C. P-partitions and the plactic congruence. Graphs Combin. 9 1 (1993) 63-73
12. C. Malvenuto, Produits et coproduits des fonctions quasi-symétriques et de l'algèbre des descentes, Publications du Laboratoire de Combinatoire et d'Informatique Mathématique, vol. 16, Ph.D. Thesis, Laboratoire de Combinatoire et d'Informatique Mathématique, Université du Québec à Montréal, 1993.
13. Malvenuto C., and Reutenauer C. Duality between quasi-symmetric functions and the Solomon descent algebra. J. Algebra 177 3 (1995) 967-982
14. P. McNamara, Edge labellings of partially ordered sets, Ph.D. Thesis, Massachusetts Institute of Technology, 2003. 〈http://www.lacim.uqam.ca/∼mcnamara/research.html〉.
15. A. Postnikov, Affine approach to quantum Schubert calculus, Duke Math. J. 128 (3) (2005) 473-509.
16. R.P. Stanley, Ordered structures and partitions, American Mathematical Society, Providence, RI, 1972, Memoirs of the American Mathematical Society, No. 119.
17. R.P. Stanley, Enumerative Combinatorics, vol. I, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986 (second printing, Cambridge University Press, Cambridge, New York, 1997).
18. R.P. Stanley, Enumerative combinatorics. Vol. 2, Cambridge Studies in Advanced Mathematics, vol. 62, Cambridge University Press, Cambridge, 1999.
19. R.P. Stanley, Errata and addenda to Enumerative combinatorics, vol. 1 (second printing) 〈http://www-math.mit.edu/∼rstan/ec/newerr.ps〉 version of 9th April 2003 or later.
20. Stanley R.P. Recent developments in algebraic combinatorics. Israel J. Math. 143 (2004) 317-339
21. J.R. Stembridge, SF, posets and coxeter/weyl, available from 〈http://www.math.lsa.umich.edu/∼jrs/maple.html〉.
22. Thibon J.-Y. Coproduits de fonctions symétriques. C.R. Acad. Sci. Paris Sér. I Math. 312 8 (1991) 553-556
23. Walton M.A. Fusion rules in Wess-Zumino-Witten models. Nuclear Phys. B 340 2-3 (1990) 777-790
24. A.V. Zelevinsky, Representations of finite classical groups, Lecture Notes in Mathematics, vol. 869, Springer, Berlin, 1981 (a Hopf algebra approach).