کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8904891 1633759 2018 47 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties
ترجمه فارسی عنوان
نظم فاصله واحد و عمل نقطه بر روی همخونی تناسلی به طور منظم هسنبرگ
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی
Our proof uses the local invariant cycle theorem of Beilinson-Bernstein-Deligne to obtain a surjection, which we call the local invariant cycle map, from the cohomology of a regular Hessenberg variety of Jordan type λ to a space of local invariant cycles. As λ ranges over all partitions, the local invariant cycles collectively contain all the information about the dot action on a regular semisimple Hessenberg variety. We then prove a result showing that, under suitable hypotheses, the local invariant cycle map is an isomorphism if and only if the special fiber has palindromic cohomology. (This is a general theorem, which is independent of the Hessenberg variety context.) Applying this result to the universal family of Hessenberg varieties, we show that, in our case, the surjections are actually isomorphisms, thus reducing the Shareshian-Wachs conjecture to computing the cohomology of a regular Hessenberg variety. But this cohomology has already been described combinatorially by Tymoczko, and, using a new reciprocity theorem for certain quasisymmetric functions, we show that Tymoczko's description coincides with the combinatorics of the chromatic quasisymmetric function.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 329, 30 April 2018, Pages 955-1001
نویسندگان
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