Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representati...Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper.展开更多
The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second comm...The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.展开更多
The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter gr...The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter group is found. The new base is described by using the notion of cell datum of Graham and Lehrer and the notion of norm.展开更多
is the disjoint union of for all , where is the set of all roots of primitive second degree equations , with reduced discriminant equal to k2m. We study the action of two Hecke groups—the full modular group and the g...is the disjoint union of for all , where is the set of all roots of primitive second degree equations , with reduced discriminant equal to k2m. We study the action of two Hecke groups—the full modular group and the group of linear-fractional transformations on . In particular, we investigate the action of on for finding different orbits.展开更多
Let A be a tame Hecke algebra of type A. A new minimal projective bimodule resolution for A is constructed and the dimensions of all the Hochschild homology groups and cyclic homology groups are calculated explicitly.
Shimura has studied the structure of the Hecke ring R(Δ,Γ) in the case Γ=SLn(Z)andΔΓis a subsemigroup of G =GLn(Q).Letpbe a prime and letΓ =GLn(Zp) Δ G =GLn( p),whereΔis a semigroup. In this paper, we shall ...Shimura has studied the structure of the Hecke ring R(Δ,Γ) in the case Γ=SLn(Z)andΔΓis a subsemigroup of G =GLn(Q).Letpbe a prime and letΓ =GLn(Zp) Δ G =GLn( p),whereΔis a semigroup. In this paper, we shall determine the structure of the Hecke ringR(Δ,Γ)and its some properties.展开更多
introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality relate...introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups.We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.展开更多
基金Supported by National Natural Science Foundation of China (11871258)the Young Backbone Teachers in Henan Province (2020GGJS194)the Young Backbone Teachers in Luoyang Normal College (2019XJGGJS-10)。
基金partially supported by Natural Sciences Foundation of China (10671193)
文摘Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper.
文摘The authors consider the extended Hecke groups H(γq) generated by T(z) = -1 / z, S(z) = -1(z +γq) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(γq), the second commutator subgroup H''(γq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups .H(γq) are studied. Also, relations between them are given.
文摘The concept of norm and cellular algebra are introduced and then the cellular basis is used to replace the Kazhdan-Lusztig basis. So a new base for the center of generic Hecke algebra associated with finite Coxeter group is found. The new base is described by using the notion of cell datum of Graham and Lehrer and the notion of norm.
文摘is the disjoint union of for all , where is the set of all roots of primitive second degree equations , with reduced discriminant equal to k2m. We study the action of two Hecke groups—the full modular group and the group of linear-fractional transformations on . In particular, we investigate the action of on for finding different orbits.
文摘Let A be a tame Hecke algebra of type A. A new minimal projective bimodule resolution for A is constructed and the dimensions of all the Hochschild homology groups and cyclic homology groups are calculated explicitly.
基金National Natural Science Foundation of China ( No.11071110)Natural Science Foundation of Jiangsu Province, China(No.BK2010362)
文摘Shimura has studied the structure of the Hecke ring R(Δ,Γ) in the case Γ=SLn(Z)andΔΓis a subsemigroup of G =GLn(Q).Letpbe a prime and letΓ =GLn(Zp) Δ G =GLn( p),whereΔis a semigroup. In this paper, we shall determine the structure of the Hecke ringR(Δ,Γ)and its some properties.
基金supported by the National Natural Science Foundation of China(NSFC)Grant 12071136.
文摘introduce the doubled Hecke algebra,which is an infinite-dimensional algebra generated by two Hecke algebras.This concept originates from the degenerate doubled Hecke algebra in the theory of Schur-Weyl duality related to enhanced reductive algebraic groups.We study the finite-dimensional natural representation of the doubled Hecke algebra on tensor space and prove that the doubled Hecke algebra forms a duality with the quantum group of Levi type.
