ncku-talk2012-05-17

NCTS(South)/ NCKU Math Colloquium

DATE 2012-05-17　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Shih-chang Huang (黃世昌教授)（國立成功大學數學系）

TITLE On the decomposition numbers of Steinberg's triality groups 3D4(2n)

ABSTRACT Let G be the simple Steinberg's triality groups 3D4(q), where q is power of prime p. The investigation of the decomposition numbers of G was begun by M. Geck. He computed the l-modular decomposition matrices of G in all odd characteristics l 6= p explicitly up to a few entries and calculated an approximation to the 2-modular decomposition matrix. In 2007, F. Himstedt determined the 2-modular decomposition matrix of G except for two entries in the Steinberg character. The case for p = 2 is still an open question.
The goal of this talk is to report a recent joint work with F. Himstedt on the decomposition numbers of 3D4(2n). We determine the l-modular decomposition matrices of 3D4(2n) for all primes l 6= 2 except for some entries in the unipotent characters. As an application, we use the decomposition matrices to classify all absolutely irreducible representations of 3D4(2n) in non-dening characteristic up to a certain degree, solving a problem proposed by P. H. Tiep and A. E. Zalesskii.

NCTS(South)/ NCKU Math Colloquium

DATE	2012-05-17　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Shih-chang Huang (黃世昌教授)（國立成功大學數學系）

TITLE	On the decomposition numbers of Steinberg's triality groups 3D4(2n)

ABSTRACT	Let G be the simple Steinberg's triality groups 3D4(q), where q is power of prime p. The investigation of the decomposition numbers of G was begun by M. Geck. He computed the l-modular decomposition matrices of G in all odd characteristics l 6= p explicitly up to a few entries and calculated an approximation to the 2-modular decomposition matrix. In 2007, F. Himstedt determined the 2-modular decomposition matrix of G except for two entries in the Steinberg character. The case for p = 2 is still an open question. The goal of this talk is to report a recent joint work with F. Himstedt on the decomposition numbers of 3D4(2n). We determine the l-modular decomposition matrices of 3D4(2n) for all primes l 6= 2 except for some entries in the unipotent characters. As an application, we use the decomposition matrices to classify all absolutely irreducible representations of 3D4(2n) in non-dening characteristic up to a certain degree, solving a problem proposed by P. H. Tiep and A. E. Zalesskii.