## Commuting families in Hecke and Temperley-Lieb Algebras

Last update: 29 January 2014

## References

[Ari2002] S. Ariki, Representations of quantum algebras and combinatorics of Young tableaux, University Lecture Series 26 Amer. Math. Soc., Providence, RI, 2002. ISBN: 0-8218- 3232-8, MR1911030 (2004b:17022)

[Che1987] I. Cherednik, A new interpretation of Gel’fand-Tzetlin bases, Duke Math. J. 54 (1987), 563–577.

[Dri1990] V.G. Drinfel'd, On almost cocommutative Hopf algebras, Leningrad Math. J. 1 (1990) 321-342. MR1025154

[Dix1996] J. Dixmier, Enveloping algebras, Graduate Studies in Mathematics 11, American Mathematical Society, Providence, RI, 1996. ISBN: 0-8218-0560-6, MR1393197 (97c:17010)

[FHa1991] W. Fulton and J. Harris, Representation theory, A first course, Graduate Texts in Mathematics 129, Springer-Verlag, New York, 1991, ISBN: 0-387-97527-6; 0-387-97495- 4, MR1153249 (93a:20069)

[GHJ1989] F. Goodman, P. de la Harpe, V.F.R. Jones, Coxeter Graphs and Towers of Algebras, Mathematical Sciences Research Institute Publications, vol. 14, Springer-Verlag, New York, 1989. MR0999799

[GLe2004] J. Graham and G. Lehrer, Cellular and diagram algebras in representation theory, in Representation theory of algebraic groups and quantum groups, Adv. Stud. Pure Math. 40 Math. Soc. Japan, Tokyo (2004) 141–173. MR2074593 (2005i:20005)

[Gro9907129] I. Grojnowski, Affine ${𝔰𝔩}_{p}$ controls the representation theory of the symmetric group and related Hecke algebras, arXiv:math.RT/9907129

[Jim1986] M. Jimbo, A $q\text{-analog}$ of $U\left(gl\left(N+1\right)\right),$ Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247-252, MR0841713 (87k:17011)

[Kle2165457] A. Kleshchev, Linear and projective representations of symmetric groups, Cambridge Tracts in Mathematics, 163, Cambridge University Press, Cambridge, 2005, xiv+277 pp.. ISBN: 0-521-83703-0, MR2165457 (2007b:20022).

[LRa1977] R. Leduc and A. Ram, A ribbon Hopf algebra approach to the irreducible representations of centralizer algebras: The Brauer, Birman-Wenzl and type A Iwahori-Hecke algebras, Adv. in Math. 125 (1997), 1-94. MR1427801 (98c:20015)

[Mac1995] I.G. Macdonald, Symmetric functions and Hall polynomials, Oxford University Press, New York (second edition, 1995).

[ORa0401317] R. Orellana and A. Ram, Affine braids, Markov traces and the category $𝒪$, in Proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces Mumbai 2004, V.B. Mehta ed., Tata Institute of Fundamental Research, Narosa Publishing House, Amer. Math. Soc. (2007), 423–473. MR2348913 arXiv:math/0401317

[OVe1996] A. Okounkov and A. Vershik, A new approach to representation theory of symmetric groups, Selecta Math. (N.S.) 2 no. 4 (1996) 581–605, MR1443185 (99g:20024)

[Ram0401326] A. Ram, Skew shape representations are irreducible, in Combinatorial and Geometric representation theory, S.-J. Kang and K.-H. Lee eds., Contemp Math. 325 Amer. Math. Soc. 2003, 161-189, MR1988991 (2004f:20014) arXiv:math.RT/0401326.

[Res1987] N. Yu. Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links $I$, LOMI Preprint no. E-4-87 (1987).

## Notes and references

This is a typed version of Commuting families in Hecke and Temperley-Lieb Algebras by Tom Halverson, Manuela Mazzocco and Arun Ram.

AMS Subject Classifications: Primary 20G05; Secondary 16G99, 81R50, 82B20.