کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11016752 | 1751025 | 2019 | 59 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Skew divided difference operators in the Nichols algebra associated to a finite Coxeter group
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let (W,S) be a finite Coxeter system with root system R and with set of positive roots R+. For αâR, v,wâW, we denote by âα, âw and âw/v the divided difference operators and skew divided difference operators acting on the coinvariant algebra of W. Generalizing the work of Liu [15], we prove that âw/v can be written as a polynomial with nonnegative coefficients in âα where αâR+. In fact, we prove the stronger and analogous statement in the Nichols-Woronowicz algebra model for Schubert calculus on W after Bazlov [4]. We draw consequences of this theorem on saturated chains in the Bruhat order, and partially treat the question when âw/v can be written as a monomial in âα where αâR+. In an appendix, we study related combinatorics on shuffle elements and Bruhat intervals of length two.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 517, 1 January 2019, Pages 19-77
Journal: Journal of Algebra - Volume 517, 1 January 2019, Pages 19-77
نویسندگان
Christoph Bärligea,