کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4583934 1630463 2016 44 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Restrictions of rainbow supercharacters
ترجمه فارسی عنوان
محدودیت سوپرچرخ های رنگین کمان
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

The maximal subgroup of unipotent upper-triangular matrices of the finite general linear groups is a fundamental family of p-groups. Their representation theory is well known to be wild, but there is a standard supercharacter theory, replacing irreducible representations by super-representations, that gives us some control over its representation theory. While this theory has a beautiful underlying combinatorics built on set partitions, the structure constants of restricted super-representations remain mysterious. This paper proposes a new approach to solving the restriction problem by constructing natural intermediate modules that help “factor” the computation of the structure constants. We illustrate the technique by solving the problem completely in the case of rainbow supercharacters (and some generalizations). Along the way we introduce a new q-analogue of the binomial coefficients that depend on an underlying poset.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 451, 1 April 2016, Pages 357–400
نویسندگان
, ,