In this paper,we completely classify a finite number of inequivalent indecom-posable modular representations of the dihedral group D2m in characteristic p,pl2m,and determine that there exists a summand of the group al...In this paper,we completely classify a finite number of inequivalent indecom-posable modular representations of the dihedral group D2m in characteristic p,pl2m,and determine that there exists a summand of the group algebra which is not a summand of the rings of coinvariants of these representations.展开更多
We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbit...We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.展开更多
In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster de...In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.展开更多
基金NNSF(12171194)of ChinaNatural Science Foundation for Young Scientists of Shanxi Province(201901D211184)Natural Science Foundation for Young Scientists(12101375).
文摘In this paper,we completely classify a finite number of inequivalent indecom-posable modular representations of the dihedral group D2m in characteristic p,pl2m,and determine that there exists a summand of the group algebra which is not a summand of the rings of coinvariants of these representations.
基金the Japan Society for Promotion of Science （JSPS）, Grant-in-Aid for Scientific Research （C）15K04776, 2015-2018, and by the CIB in EPFL. The second author was supported by the German Science Foundation （DFG） Scientific Priority Programme SPP-1489 ＂Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory＂.
文摘We give a lower bound of the Loewy length of the projective cover of the trivial module for the group algebra kG of a finite group G of Lie type defined over a finite field of odd characteristic p, where k is an arbitrary field of characteristic p. The proof uses Auslander-Reiten theory.
基金supported by National Natural Science Foundation of China(Grant No.11901586)the Natural Science Foundation of Guangdong Province(Grant No.2019A1515011323)the Sun Yat-sen University Research Grant for Youth Scholars(Grant No.19lgpy244)。
文摘In this work, we show that the difference of a Hauptmodul for a genus zero group Γ_(0)(N) as a modular function on Y_(0)(N) × Y_(0)(N) is a Borcherds lift of type(2, 2). As applications, we derive the monster denominator formula like product expansions for these modular functions and certain Gross-Zagier type CM value formulas.
