Representations of the q-rook monoid

Journal of Algebra

Volumn 273, Issue 1, 2004, Pages 227-251

  Halverson, Tom ^a  

^a MACALESTER COLLEGE   (United States)

Author keywords

Iwahori Hecke algebra; Quantum group; Representation; Rook monoid

Indexed keywords

EID: 1342268343     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jalgebra.2003.11.002     Document Type: Article

References (22)

1. V. Chari, A. Pressley, A Guide to Quantum Groups, Cambridge Univ. Press, 1994.
2. C. Curtis, I. Reiner, Methods of Representation Theory: With Applications to Finite Groups and Orders, vol. I, Wiley, New York, 1981.
3. C. Curtis, I. Reiner, Methods of Representation Theory: With Applications to Finite Groups and Orders, vol. II, Wiley, New York, 1987.
4. M. Dieng, T. Halverson, V. Poladian, Character formulas for q-rook monoid algebras, J. Algebraic Combin. 17 (2003) 99-123.
5. C. Grood, A Specht module analog for the rook monoid, Electron. J. Combin. 9 (2002) 10 (electronic).
6. T. Halverson, A. Ram, q-rook monoid algebras, Hecke algebras, and Schur-Weyl duality, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 283 (2001) 224-250.
7. P.N. Hoefsmit, Representations of Hecke algebras of finite groups with BN-pairs of classical type, Thesis, Univ. of British Columbia, 1974.
8. N. Iwahori, On the structure of a Hecke ring of a Chevalley group over a finite field, J. Fac. Sci. Univ. Tokyo, Sec. I 10 (1664) 215-236.
9. M. Jimbo, A q-analog of U(gl(N + 1)), Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986) 247-252.
10. S. Lipscomb, Symmetric Inverse Semigroups, in: Math. Surveys Monogr., vol. 46, Amer. Math. Soc., Providence, RI, 1996.
11. I.G. Macdonald, Symmetric Functions and Hall Polynomials, Second edition, Oxford Univ. Press, New York, 1995.
12. E.H. Moore, Concerning the abstract groups of order k! and 1/2k! holohedrically isomorphic with the symmetric and the alternating substitution groups on k letters, Proc. London Math. Soc. 28 (1897) 357-366.
13. W.D. Munn, Matrix representations of semigroups, Proc. Cambridge Philos. Soc. 53 (1957) 5-12.
14. W.D. Munn, The characters of the symmetric inverse semigroup, Proc. Cambridge Philos. Soc. 53 (1957) 13-18.
15. J. Okniński, M. Putcha, Complex representations of matrix semigroups, Trans. Amer. Math. Soc. 323 (1991) 563-581.
16. M. Putcha, Monoid Hecke algebras, Trans. Amer. Math. Soc. 349 (1997) 3517-3534.
17. A. Ram, Seminormal representations of Weyl groups and Iwahori-Hecke algebras, Proc. London Math. Soc. (3) 75 (1997) 99-133.
18. L. Renner, Analog of the Bruhat decomposition for algebraic monoids II. The length function and trichotomy, J. Algebra 175 (1995) 697-714.
19. 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.
20. L. Solomon, Representations of the rook monoid, J. Algebra 256 (2002) 309-342.
21. q). A presentation and a representation on tensor space, J. Algebra 273 (2004) 206-226, this issue.
22. A. Young, On quantitative substitutional analysis VI, Proc. London Math. Soc. 31 (1931) 253-289.