On the Multivariate Robinson-Schensted Correspondence

Fabrizio Caselli

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 3, page 591-602
  • ISSN: 0392-4041

Abstract

top
We show the existence of a multivariate extension of the Robinson-Schensted correspondence. This is inspired by the interpretation of the classical two dimensional case in the invariant theory of (finite) reflection groups.

How to cite

top

Caselli, Fabrizio. "On the Multivariate Robinson-Schensted Correspondence." Bollettino dell'Unione Matematica Italiana 1.3 (2008): 591-602. <http://eudml.org/doc/290468>.

@article{Caselli2008,
abstract = {We show the existence of a multivariate extension of the Robinson-Schensted correspondence. This is inspired by the interpretation of the classical two dimensional case in the invariant theory of (finite) reflection groups.},
author = {Caselli, Fabrizio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {591-602},
publisher = {Unione Matematica Italiana},
title = {On the Multivariate Robinson-Schensted Correspondence},
url = {http://eudml.org/doc/290468},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Caselli, Fabrizio
TI - On the Multivariate Robinson-Schensted Correspondence
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/10//
PB - Unione Matematica Italiana
VL - 1
IS - 3
SP - 591
EP - 602
AB - We show the existence of a multivariate extension of the Robinson-Schensted correspondence. This is inspired by the interpretation of the classical two dimensional case in the invariant theory of (finite) reflection groups.
LA - eng
UR - http://eudml.org/doc/290468
ER -

References

top
  1. ADIN, R. - BRENTI, F. - ROICHMAN, Y., Descent representations and multivariate statistics, Trans. Amer. Math. Soc., 357, no. 8 (2005), 3051-3082. Zbl1059.05105MR2135735DOI10.1090/S0002-9947-04-03494-4
  2. ADIN, R. - ROICHMAN, Y., The flag major index and group actions on polynomial rings, Europ. J. Combin., 22 (2001), 431-446. Zbl1058.20031MR1829737DOI10.1006/eujc.2000.0469
  3. BAGNO, E. - BIAGIOLI, R., Colored-descent representations of complex reflection groups G ( r , p , n ) . Israel J. Math., 160 (2007), 317-347. Zbl1178.20003MR2342500DOI10.1007/s11856-007-0065-z
  4. BARCELO, H. - REINER, V. - STANTON, D., Bimahonian distributions, preprint (arXiv CO/0703479v1), 2007. MR2418296DOI10.1112/jlms/jdn004
  5. BESSENRODT, C. - KLESHCHEV, A., On Kronecker products of complex representations of the symmetric and alternating groups, Pacific J. Math., 190, no. 2 (1999), 201-223. Zbl1009.20013MR1722888DOI10.2140/pjm.1999.190.201
  6. BIAGIOLI, R. - CASELLI, F., Invariant algebras and major indices for classical Weyl groups, Proc. London Math. Soc. (3) 88, no. 3 (2004), 603-631. Zbl1067.05077MR2044051DOI10.1112/S0024611503014552
  7. BIAGIOLI, R. - CASELLI, F., A descent basis for the coinvariant algebra of type D. J. Algebra, 275, no. 2 (2004), 517-539. Zbl1079.05518MR2052623DOI10.1016/j.jalgebra.2003.12.022
  8. CHEVALLEY, C., Invariants of finite groups generated by reflections, Amer. J. Math., 77 (1955), 778-782 Zbl0065.26103MR72877DOI10.2307/2372597
  9. DVIR, Y., On the Kronecker product of S n characters, 1J. Algebra, 154, no. 1 (1993), 125-140. Zbl0848.20006MR1201916DOI10.1006/jabr.1993.1008
  10. GARSIA, A. - GESSEL, I., Permutation statistics and partitions, Adv. Math., 31 (1979) 288-305. Zbl0431.05007MR532836DOI10.1016/0001-8708(79)90046-X
  11. GORDON, B., Two theorems on multipartite partitions, J. London Math. Soc., 38 (1963), 459-464. Zbl0119.04105MR157959DOI10.1112/jlms/s1-38.1.459
  12. W.KRAŚKIEWICZ - WEYMAN, J., Algebra of coinvariants and the action of a Coxeter element, Bayreuth. Math. Schr. no. 63 (2001), 265-284. Zbl1037.20012MR1867283
  13. MACMAHON, P. A., Combinatory analysis, vol. 1, Cambridge University Press, London, 1915. MR141605
  14. REGEV, A., On the height of the Kronecker product of S n characters, Israel J. Math., 42, no. 1-2 (1982), 60-64. Zbl0507.20011MR687934DOI10.1007/BF02765010
  15. ROBINSON, G. DE B., On the representations of the symmetric group, Amer. J. Math., 60, no. 3 (1938), 745-760. Zbl64.0070.01MR1507943DOI10.2307/2371609
  16. SCHENSTED, C., Longest increasing and decreasing subsequences, Canad. J. Math., 13 (1961), 179-191. Zbl0097.25202MR121305DOI10.4153/CJM-1961-015-3
  17. SHEPHARD, G. C. - TODD, J. A., Finite unitary reflection groups, Canadian J. Math., 6 (1954) 274-304. Zbl0055.14305MR59914
  18. STANLEY, R. P., Enumerative combinatorics, vol. 2, Cambridge Studies in Advanced Mathematics62, Cambridge University Press, Cambridge, 1999. MR1676282DOI10.1017/CBO9780511609589
  19. STEMBRIDGE, J.R., On the eigenvalues of representations of reflection groups and wreath products. Pacific J. Math., 140, no. 2 (1989), 353-396. Zbl0641.20011MR1023791

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.