Elias,et al.(2016)conjectured that the Kazhdan-Lusztig polynomial of any matroid is logconcave.Inspired by a computer proof of Moll’s log-concavity conjecture given by Kauers and Paule,the authors use a computer alge...Elias,et al.(2016)conjectured that the Kazhdan-Lusztig polynomial of any matroid is logconcave.Inspired by a computer proof of Moll’s log-concavity conjecture given by Kauers and Paule,the authors use a computer algebra system to prove the conjecture for arbitrary uniform matroids.展开更多
In this paper we show that the leading coeficient μ(y,w) of some Kazhdan-Lusztig polynomials Py,w with y,w in an affine Weyl group of type n is n + 2.This fact has some consequences on the dimension of first extensio...In this paper we show that the leading coeficient μ(y,w) of some Kazhdan-Lusztig polynomials Py,w with y,w in an affine Weyl group of type n is n + 2.This fact has some consequences on the dimension of first extension groups of finite groups of Lie type with irreducible coefficients.展开更多
Canonical bases of the tensor powers of the natural Uq(glm|n)-module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several di...Canonical bases of the tensor powers of the natural Uq(glm|n)-module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several directions. We first construct the canonical bases of the Z2-graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra Oq(Mm|n) of a quantum (m, n) × (m, n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for Uq(glm|n) by applying a quantum analogue of the Borel-Weil construction.展开更多
Let(W,S)be the affine Weyl group of type B_(2),on which we consider the length function e from W to N and the Bruhat order≤.For y<w in W,letμ(y,w)be the coefficient of q^(1/2(e(w)-e(y)-1)) in Kazhdan-Lusztig poly...Let(W,S)be the affine Weyl group of type B_(2),on which we consider the length function e from W to N and the Bruhat order≤.For y<w in W,letμ(y,w)be the coefficient of q^(1/2(e(w)-e(y)-1)) in Kazhdan-Lusztig polynomial P_(y,w)∈Z[q].We determine someμ(y,w)for y∈c_(0) and w∈c_(2),where c0 is the lowest two-sided cell of B_(2) and c_(2) is the higher one.Furthermore,we get some consequences using left or right strings and some properties of leading coefficients.展开更多
In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-her...In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,...,n} such that HomB(P(i),P(j)) = 0 for i > j.In this paper,it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l,then its dual extension algebra A = A(B) has also the Kazhdan-Lusztig theory relative to the length function l.展开更多
We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring A = Z[g^1/2, q^-1/2], where q is an indeterminate)...We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring A = Z[g^1/2, q^-1/2], where q is an indeterminate) using C-bases for these modules. Moreover, we provide a link bet ween a certain C-basis for the induced Specht module and the notion of pairs of partitions.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11901431 and 12171362.
文摘Elias,et al.(2016)conjectured that the Kazhdan-Lusztig polynomial of any matroid is logconcave.Inspired by a computer proof of Moll’s log-concavity conjecture given by Kauers and Paule,the authors use a computer algebra system to prove the conjecture for arbitrary uniform matroids.
基金supported by National Natural Science Foundation of China (Grant No.10671193)
文摘In this paper we show that the leading coeficient μ(y,w) of some Kazhdan-Lusztig polynomials Py,w with y,w in an affine Weyl group of type n is n + 2.This fact has some consequences on the dimension of first extension groups of finite groups of Lie type with irreducible coefficients.
基金supported by National Natural Science Foundation of China (Grant No. 10471070)
文摘Canonical bases of the tensor powers of the natural Uq(glm|n)-module V are constructed by adapting the work of Frenkel, Khovanov and Kirrilov to the quantum supergroup setting. This result is generalized in several directions. We first construct the canonical bases of the Z2-graded symmetric algebra of V and tensor powers of this superalgebra; then construct canonical bases for the superalgebra Oq(Mm|n) of a quantum (m, n) × (m, n)-supermatrix; and finally deduce from the latter result the canonical basis of every irreducible tensor module for Uq(glm|n) by applying a quantum analogue of the Borel-Weil construction.
基金Supported in part by the Natural Science Foundation of China(Grant no.11101233)Beijing Youth Top-notch Talent Support Program(Grant no.21351918007).
文摘Let(W,S)be the affine Weyl group of type B_(2),on which we consider the length function e from W to N and the Bruhat order≤.For y<w in W,letμ(y,w)be the coefficient of q^(1/2(e(w)-e(y)-1)) in Kazhdan-Lusztig polynomial P_(y,w)∈Z[q].We determine someμ(y,w)for y∈c_(0) and w∈c_(2),where c0 is the lowest two-sided cell of B_(2) and c_(2) is the higher one.Furthermore,we get some consequences using left or right strings and some properties of leading coefficients.
基金the Foundation of Zhangzhou Normal University (No.SK05012)
文摘In order to study the representation theory of Lie algebras and algebraic groups,Cline,Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasi-hereditary algebras.Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,...,n} such that HomB(P(i),P(j)) = 0 for i > j.In this paper,it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l,then its dual extension algebra A = A(B) has also the Kazhdan-Lusztig theory relative to the length function l.
文摘We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring A = Z[g^1/2, q^-1/2], where q is an indeterminate) using C-bases for these modules. Moreover, we provide a link bet ween a certain C-basis for the induced Specht module and the notion of pairs of partitions.
