Representations of the rook monoid

Journal of Algebra

Volumn 256, Issue 2, 2002, Pages 309-342

  Solomon, Louis ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037110385     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(02)00004-2     Document Type: Article

References (20)

1. D. Easdown, A monoid presentation of the symmetric inverse semigroup, Unpublished manuscript, 1991.
2. C. Grood, A Specht module analogue for the rook monoid, Electron. J. Combin. 9 (1) (2002), Research Paper 2.
3. T. Halverson, Representations of the q-rook monoid, Preprint, 2001.
4. P.M. Higgins, Techniques of Semigroup Theory, Oxford University Press, 1992.
5. L.C. Hsu, Note on a pair of combinatorial reciprocal formulas, Math. Student 22 (1954) 175-178.
6. S. Lipscomb, Symmetric Inverse Semigroups, in: Math. Surveys Monographs. Vol. 46, American Mathematical Society, 1996.
7. I.G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd Edition, Clarendon Press, Oxford, 1995.
8. E.H. Moore, Concerning the abstract groups of order k! and 1/2 k! holohedrically isomorphic with the symmetric and alternating substitution groups on k letters, Proc. London Math. Soc. 28 (1897) 357-366.
9. W.D. Munn, Matrix representations of semigroups, Proc. Cambridge Philos. Soc. 53 (1957) 5-12.
10. W.D. Munn, The characters of the symmetric inverse semigroup, Proc. Cambridge Philos. Soc. 53 (1957) 13-18.
11. L.M. Popova, Defining relations of certain semigroups of partial transformations of a finite set, Uchen. Zap. Leningrad. Gos. Ped. Inst. 218 (1961) 191-212, in Russian.
12. I. Schur, Über eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen, Dissertation. 1901. Gesammelte Abhandlungen, Band I, Springer-Verlag, 1973, pp. 1-70.
13. I. Schur, Über die rationalen Darstellungen der allgemeinen lineare Gruppe, Sitz. Preuss. Akad. Wiss. Phys.-Math. Klasse (1927), Gesammelte Abhandlungen, Band III, Springer-Verlag, 1973, pp. 68-85.
14. L. Solomon, The Burnside algebra of a finite group, J. Combin. Theory 2 (1967) 603-615.
15. L. Solomon, The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field, Geom. Dedicata 36 (1990) 15-49.
16. q): A presentation and a representation on tensor space, preprint 2002.
17. R. Stanley, Enumerative Combinatorics, Vol. I, Wadsworth & Brooks Cole, 1986, reprinted by Cambridge Univ, Press.
18. G. Walker, The actions of the divided differential operator algebra and the symmetric inverse semigroup on polynomials, unpublished manuscript, 1997.
19. H. Weyl, Theorie der Darstellung kontinuierlicher halbeinfacher Gruppen durch lineare Transformationen, I, Math. Z. 23 (1925) 271-309, Gesammelte Abhandlungen, Band II, Springer-Verlag, 1968, pp. 543-579.
20. H. Weyl, The Classical Groups, 2nd Edition, Princeton University Press, 1946.