کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771887 | 1630430 | 2017 | 35 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Twisted filtrations of Soergel bimodules and linear Rouquier complexes
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Twisted filtrations of Soergel bimodules and linear Rouquier complexes Twisted filtrations of Soergel bimodules and linear Rouquier complexes](/preview/png/5771887.png)
چکیده انگلیسی
We consider twisted standard filtrations of Soergel bimodules associated to arbitrary Coxeter groups and show that the graded multiplicities in these filtrations can be interpreted as structure constants in the Hecke algebra. This corresponds to the positivity of the polynomials occurring when expressing an element of the canonical basis in a generalized standard basis twisted by a biclosed set of roots in the sense of Dyer, and comes as a corollary of Soergel's conjecture. We then show the positivity of the corresponding inverse polynomials in the case where the biclosed set is an inversion set of an element or its complement by generalizing a result of Elias and Williamson on the linearity of the Rouquier complexes associated to lifts of these basis elements in the Artin-Tits group. These lifts turn out to be generalizations of Mikado braids as introduced in a joint work with Digne. This second positivity property generalizes a result of Dyer and Lehrer from finite to arbitrary Coxeter groups.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 484, 15 August 2017, Pages 275-309
Journal: Journal of Algebra - Volume 484, 15 August 2017, Pages 275-309
نویسندگان
Thomas Gobet,