Tight Monomials In Quantum Group For Type B₃

Quantum group (also called quantized enveloping algebra) has found numerous deeply applications in areas ranging from theoretical physics via symplectic geometry and knot theory to modular representations of reductive algebraic groups. It has many classes of bases, which the most powerful one is Canonical basis, and the simplest elements in Canonical basis are monomials. We compute all the tight monomials with t-value≤6in quantum group for type B3in this paper.This paper is divided into five chapters:In the first chapter, we introduce the background of quantum group and Canonical basis of quantum group, and present the source of this paper.In the second chapter, we recall some concepts about quantum group and algebraic definition of Canonical basis of quantum group.In the third chapter, we list the known results about Canonical basis of quantum group.In the fourth chapter, we compute all the tight monomials with i-value<6in quantum group for type B3.In the fifth chapter, we prove the results in chapter4.