Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root...Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root system R(m,p,n)of G(m,p,n).展开更多
Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an inter...Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an interpretation in terms of Lusztig's partition function. Finkelberg and Ionov(2016) defined alternate functions K_(λ,μ)(t) by using an analogue of Lusztig's partition function, and showed that K_(λ,μ)(t) ∈Z≥0[t] for generic μ by making use of a coherent realization. They conjectured that K_(λ,μ)(t) coincide with K_(λ,μ)^-(t). In this paper, we show that their conjecture holds. We also discuss the multi-variable version, namely, r-variable Kostka functions K_(λ,μ)~±(t_1,…,t_r).展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.10631010,10971138)the General Research Project of Shanghai Normal University(Grant No.SK200702)+2 种基金the Science Foundation of University Doctoral Project of China(Grant No.20060269011)Program for Changjiang Scholars and Innovative Research Team in University(Grant No.41192803)Shanghai Leading Academic Discipline Project(Grant No.B407)
文摘Based on a graph-theoretic analysis,we determine all the irreducible reflection subgroups of the imprimitive complex reflection groups G(m,p,n),and describe the irreducible subsystems of all possible types in the root system R(m,p,n)of G(m,p,n).
文摘Kostka functions K_(λ,μ)~±(t), indexed by r-partitions λ and μ of n, are a generalization of Kostka polynomials K_(λ,μ)(t) indexed by partitions λ,μ of n. It is known that Kostka polynomials have an interpretation in terms of Lusztig's partition function. Finkelberg and Ionov(2016) defined alternate functions K_(λ,μ)(t) by using an analogue of Lusztig's partition function, and showed that K_(λ,μ)(t) ∈Z≥0[t] for generic μ by making use of a coherent realization. They conjectured that K_(λ,μ)(t) coincide with K_(λ,μ)^-(t). In this paper, we show that their conjecture holds. We also discuss the multi-variable version, namely, r-variable Kostka functions K_(λ,μ)~±(t_1,…,t_r).
