Tight monomials for type B₃

Abstract

The global crystal basis or canonical basis plays an important role in the theory of the quantized enveloping algebras and their representations. The tight monomials are the simplest elements in the canonical basis. We discuss the tight monomials in quantized enveloping algebra of type B₃.

Keywords

Quantized enveloping algebra / canonical basis / tight monomial

References

[1] Caldero P, Marsh R, Morier-Genoud S. Realisation of Lusztig cones. Represent Theory, 2004, 8: 458-478

[2] Deng B, Du J. Tight monomials and the monomial basis property. J Algebra, 2010, 324: 458-478

[3] Deng B, Du J, Parashall B, Wang J. Finite Dimensional Algebras and Quantum Groups. Mathematical Surveys and Monographs, Vol 150. Providence: Amer Math Soc, 2008

[4] Hu Y, Ye J, Yue X. Canonical basis for type A₄—monomial elements. J Algebra, 2003, 263: 228-245

[5] Lusztig G. Canonical bases arising from quantized enveloping algebras. J Amer Math Soc, 1990, 3: 447-498

[6] Lusztig G. Quivers, perverse sheaves, and the quantized enveloping algebras. J Amer Math Soc, 1991, 4: 366-421

[7] Lusztig G. Tight monomials in quantized enveloping algebras. Israel Math Conf Proc, 1993, 7: 117-132

[8] Lusztig G. Introduction to Quantum Groups. Boston: Birkhäuser, 1993

[9] Marsh R. More tight monomials in quantized enveloping algebras. J Algebra, 1998, 204: 711-732

[10] Reineke M. Monomials in canonical bases of quantum groups and quadratic forms. J Pure Appl Algebra, 2001, 157: 301-309

[11] Wang X. Tight monomials for type G₂ and A₃.Comm Algebra, 2010, 38: 3597-3615

[12] Wang X. Tight monomials for quantum enveloping algebras of rank-2 Kac-Moody Lie algebras. J Pure Appl Algebra, 2012, 216: 694-708

[13] Xi N. Canonical basis for type B₂.J Algebra, 1999, 214: 8-21

[14] Xi N. Canonical basis for type A₃.Comm Algebra, 1999, 27: 5703-5710

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg