All tight
monomials in quantum group for type A5 with t ≤ 6 are determined in this
paper.
References
[1]
Drinfel’d, V.G. (1985) Hopf Algebras and the Quantum Yang-Baxter Equation. Soviet Mathematics Doklady, 32, 254-258.
[2]
Jimbo, M. (1985) A q-Difference Analogue of and the Yang-Baxter Equation. Letters in Mathematical Physics, 10, 63-69. http://dx.doi.org/10.1007/BF00704588
[3]
Lusztig, G. (1990) Canonical Bases Arising from Quantized Enveloping Algebras. Journal of the American Mathematical Society, 3, 447-498. http://dx.doi.org/10.1090/S0894-0347-1990-1035415-6
[4]
Lusztig, G. (1993) Tight Monomials in Quantized Envelwoping Algebras. In: Joseph, A. and Schnider, S., Eds., Quantum Deformation of Algebra and Their Representations, Israel Mathematical Conference Proceedings, Vol. 7, Bar-Ilan University, 117-132.
[5]
Xi, N.H.(1999) Canonical Basis for Type A3. Communications in Algebra, 27, 5703-5710. http://dx.doi.org/10.1080/00927879908826784
[6]
Hu, Y.W., Ye, J.C. and Yue, X.Q. (2003) Canonical Basis of Type A4 (I)-Monomial Elements. Journal of Algebra, 263, 228-245. http://dx.doi.org/10.1016/S0021-8693(03)00066-8
[7]
Hu, Y.W. and Ye, J.C. (2005) Canonical Bases of Type A4 (II)-Polynomial Elements in One Variable. Communications in Algebra, 33, 3855-3877. http://dx.doi.org/10.1080/00927870500261033
[8]
Li, X.C. and Hu, Y.W. (2012) Ploynomical Elements in Canonical Basis of Type B with Two-Dimensional Support for A4 (I). Algebra Colloquium, 19, 117-136. http://dx.doi.org/10.1142/S1005386712000089
[9]
Marsh, R. (1998) More Tight Monomials in Quantized Enveloping Algebras. Journal of Algebra, 204, 711-732. http://dx.doi.org/10.1006/jabr.1997.7370
[10]
Reineke, M. (2001) Monomials in Canonical Bases of Quantum Groups and Quadratic Forms. Journal of Pure and Applied Algebra, 157, 301-309. http://dx.doi.org/10.1016/S0022-4049(00)00008-6
[11]
Wang, X.M. (2010) Tight Monomials for Type G2 and A3. Communications in Algebra, 38, 3597-3615. http://dx.doi.org/10.1080/00927870903200919
[12]
Deng, B.M. and Du, J. (2010) Tight Monomials and Monomial Basis Property. Journal of Algebra, 324, 3355-3377. http://dx.doi.org/10.1016/j.jalgebra.2010.09.022