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@article{Re,
	Author = {Renner, L. E.},
	Date-Modified = {2017-03-26 04:36:29 +0000},
	Doi = {10.1006/jabr.1995.1208},
	Journal = {J. Algebra},
	Pages = {697--714},
	Title = {Analogue of the {B}ruhat decomposition for algebraic monoids. {II}. {T}he length function and the trichotomy},
	Volume = {175},
	Year = {1995}}

@article{Iw,
	Author = {Iwahori, N.},
	Date-Modified = {2017-03-26 04:23:04 +0000},
	Journal = {J. Fac. Sci. Univ. Tokyo Sect. I},
	Pages = {215--236},
	Title = {On the structure of a {H}ecke ring of a {C}hevalley group over a finite field},
	Volume = {10},
	Year = {1964}}

@article{So1,
	Author = {Solomon, L.},
	Date-Modified = {2017-03-26 04:37:11 +0000},
	Doi = {10.1007/bf00181463},
	Journal = {Geom. Dedicata},
	Pages = {15--49},
	Title = {The {B}ruhat decomposition, {T}its system and {I}wahori ring for the monoid of matrices over a finite field},
	Volume = {36},
	Year = {1990}}

@article{So2,
	Author = {Solomon, L.},
	Date-Modified = {2017-03-26 04:38:14 +0000},
	Doi = {10.1016/j.jalgebra.2003.08.013},
	Journal = {J. Algebra},
	Pages = {206--226},
	Title = {The {I}wahori algebra of {$\bold M_n(\bold F_q)$}. {A} presentation and a representation on tensor space},
	Volume = {273},
	Year = {2004}}

@article{Ha,
	Author = {Halverson, T.},
	Date-Modified = {2017-03-26 04:21:17 +0000},
	Doi = {10.1016/j.jalgebra.2003.11.002},
	Journal = {J. Algebra},
	Pages = {227--251},
	Title = {Representations of the {$q$}-rook monoid},
	Volume = {273},
	Year = {2004}}

@article{DHST,
	Author = {Denton, T. and Hivert, F. and Schilling, A. and Thi{\'e}ry, N. M.},
	Date-Modified = {2017-03-26 04:19:44 +0000},
	Journal = {S\'em. Lothar. Combin.},
	Pages = {Art. B64d},
	Title = {On the representation theory of finite $\mathcal{J}$-trivial monoids},
	Url = {https://www.mat.univie.ac.at/~slc/wpapers/s64dehiscth.html},
	Volume = {64},
	Year = {2011}}

@article{Norton,
	Author = {P. N. Norton},
	Date-Modified = {2017-03-26 04:28:12 +0000},
	Doi = {10.1017/S1446788700012453},
	Journal = {J. Austral. Math. Soc. Ser A.},
	Pages = {337--357},
	Title = {$0$-Hecke algebras},
	Volume = {27},
	Year = {1979}}

@article{Carter,
	Author = {R. W. Carter},
	Date-Modified = {2017-03-26 04:17:53 +0000},
	Doi = {10.1016/0021-8693(86)90238-3},
	Journal = {J. Algebra},
	Pages = {89-103},
	Title = {Representation theory of the $0$-Hecke algebra},
	Volume = {104},
	Year = {1986}}

@unpublished{Pin,
	Author = {J.-E. Pin},
	Date-Modified = {2017-03-26 04:43:54 +0000},
	Note = {Preprint},
	Title = {Mathematical Foundations of Automata Theory},
	Url = {https://www.irif.fr/~jep/PDF/MPRI/MPRI.pdf},
	Year = {2016},
	Bdsk-Url-1 = {http://www.liafa.jussieu.fr/~jep/MPRI/MPRI.html}}

@article{Fayers,
	Author = {M. Fayers},
	Date-Modified = {2017-03-26 04:20:28 +0000},
	Doi = {10.1016/j.jpaa.2004.12.001},
	Journal = {J. Pure Appl. Algebra},
	Pages = {27--41},
	Title = {$0$-Hecke algebras of finite Coxeter groups},
	Volume = {199},
	Year = {2005}}

@article{BL,
	Author = {Bergeron, N. and Li, H.},
	Date-Modified = {2017-03-26 04:17:10 +0000},
	Doi = {10.1016/j.jalgebra.2008.12.005},
	Journal = {J. Algebra},
	Pages = {2068--2084},
	Title = {Algebraic structures on Grothendieck groups of a tower of algebras},
	Volume = {321},
	Year = {2009}}

@inproceedings{Virmaux,
	Author = {A. Virmaux},
	Booktitle = {26th International Conference on Formal Power Series and Algebraic Combinatorics},
	Date-Modified = {2017-03-26 04:43:36 +0000},
	Pages = {741--752},
	Publisher = {DMTCS Proceedings},
	Title = {Partial categorification of Hopf algebras and representation theory of towers of $\mathcal{J}$-trivial monoids},
	Url = {https://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/view/dmAT0164.1.html},
	Year = {2014}}

@article{KT,
	Author = {Daniel Krob and Jean-Yves Thibon},
	Date-Modified = {2017-03-26 04:26:36 +0000},
	Doi = {10.1023/A:1008673127310},
	Journal = {J. Algebraic Combin.},
	Pages = {339--376},
	Title = {Noncommutative symmetric functions IV: Quantum linear groups and Hecke algebras at $q = 0$},
	Volume = {6},
	Year = {1997}}

@article{Huang,
	Author = {J. Huang},
	Date-Modified = {2017-03-26 04:22:28 +0000},
	Doi = {10.1007/s00026-016-0338-5},
	Journal = {Ann. Combinatorics},
	Pages = {831--868},
	Title = {A tableau approach to the representation theory of 0-Hecke algebras.},
	Volume = {20},
	Year = {2016}}