Applications of minor summation formula III, Plücker relations, lattice paths and Pfaffian identities

Journal of Combinatorial Theory. Series A

Volumn 113, Issue 1, 2006, Pages 113-155

  Ishikawa, Masao ^a   Wakayama, Masato ^b  

^a TOTTORI UNIVERSITY   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

Author keywords

Cauchy identity; Lattice paths method; Lewis Carroll formula; Minor summation formula; Partition; Pfaffian; Pl cker relations; q series; Schur function

Indexed keywords

EID: 30444443612     PISSN: 00973165     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcta.2005.05.008     Document Type: Article

References (31)

1. D.M. Bressoud, Proofs and Confirmations, Cambridge University Press, Cambridge, 1999.
2. D.M. Bressoud Identities for Schur functions and plane partitions Ramanujan J. 4 2000 69-80
3. A. Dress W. Wenzel A simple proof of an identity concerning pfaffians of skew symmetric matrices Adv. Math. 112 1995 120-134
4. I. Gessel, G. Viennot, Determinants, paths, and plane partitions, preprint, 1989.
5. A. Gyoja K. Nishiyama K. Taniguchi Kawanaka invariants for representations of Weyl groups J. Algebra 225 2000 842-871
6. R. Hirota, Mathematical aspect of the soliton theory from a direct methods point of view, Iwanami Shoten (1992) (in Japanese).
7. M. Ishikawa S. Okada M. Wakayama Applications of minor summation formulas I, Littlewood's formulas J. Algebra 183 1996 193-216
8. M. Ishikawa M. Wakayama Minor summation formula of Pfaffians Linear and Multilinear Algebra 39 1995 285-305
9. M. Ishikawa M. Wakayama Minor summation formula of Pfaffians and Schur functions identities Proc. Japan Acad. Ser. A Math Sci. 71 1995 54-57
10. M. Ishikawa M. Wakayama New Schur function series J. Algebra 208 1998 480-525
11. M. Ishikawa M. Wakayama Applications of minor summation formulas II, Pfaffians of Schur polynomials J. Combin. Theory Ser. A 88 1999 136-157
12. M. Ishikawa M. Wakayama Minor summation formula of Pfaffians, Survey and a new identity Adv. Stud. Pure Math. 28 2000 133-142
13. F. Jouhet J. Zeng Some new identities for Schur functions Adv. Appl. Math. 27 2001 493-509
14. F. Jouhet, J. Zeng, New identities of Hall-Littlewood polynomials and Applications, Ramanujan J. 10 (2005), to appear.
15. N. Kawanaka A q-series identity involving Schur functions and related topics Osaka J. Math. 36 1999 157-176
16. N. Kawanaka A q-Cauchy identity involving Schur functions and imprimitive complex reflection groups Osaka J. Math. 38 2001 775-810
17. K. Kinoshita M. Wakayama Explicit Capelli identities for skew symmetric matrices Proc. Edinburgh Math. Soc. 45 2002 449-465
18. D. Knuth Overlapping Pfaffians Electron. J. Combin. 3 1996 151-163
19. C. Krattenthaler, Advanced determinant calculus, Sem. Lotharingien Combin. vol. 42 ("The Andrews Festschrift") (1999) Article B42q, 67.
20. A. Lascoux, Littlewood's formulas for characters of orthogonal and symplectic groups, Algebraics Combin. Quantum Groups (2003).
21. J.-G. Luque J.-Y. Thibon Pfaffian and hafnian identities in shuffle algebras Adv. Appl. Math. 29 2002 620-646
22. J.-G. Luque J.-Y. Thibon Hankel hyperdeterminants and Selberg integrals J. Phys. A 36 16 May 2003 5267-5292
23. I.G. Macdonald Symmetric Functions and Hall Polynomials second ed. 1995 Oxford University Press Oxford
24. S. Okada On the generating functions for certain classes of plane partitions J. Combin. Theory Ser. A 51 1989 1-23
25. S. Okada Applications of minor-summation formulas to rectangular-shaped representations of classical groups J. Algebra 205 1998 337-367
26. D.P. Robbins H. Rumsey Jr. Determinants and alternating sign matrices Adv. Math. 62 1986 169-184
27. I. Schur Aufgabe 569 Arch. Math. Phys. 27 3 1918 163
28. R.P. Stanley, Enumerative Combinatorics, vols. I, II, Cambridge University Press, Cambridge, 1997, 1999.
29. J. Stembridge Nonintersecting paths, pfaffians and plane partitions Adv. Math. 83 1990 96-131
30. T. Sundquist Two variable Pfaffian identities and symmetric functions J. Alg. Combin. 5 1996 135-148
31. C.A. Tracy H. Widom A limit theorem for shifted Schur measures Duke Math. J. 123 2004 178-208