The left cells with a-values 5, 6 in the affine Weyl group ~E8
نویسندگان
چکیده
We describe all the left cells of a-values 5, 6 in the affine Weyl group e E8 in the paper. More precisely, we show that each of those left cells is left-connected, verifying a conjecture of Lusztig in our case. We find all the distinguished involutions in those left cells which occur as the vertices of the corresponding distinguished involution graphs. We also get all the corresponding left cell graphs.
منابع مشابه
Left Cells in Affine Weyl Groups
We prove a property of left cells in certain crystallographic groups W , by which we formulate an algorithm to find a representative set of left cells of W in any given two-sided cell. As an illustration, we make some applications of this algorithm to the case where W is the affine Weyl group of type e F4. The cells of affine Weyl groups W , as defined by Kazhdan and Lusztig in [6], have been d...
متن کاملLEFT CELLS IN THE AFFINE WEYL GROUP Wa(D̃4)
The cells of affine Weyl groups have been studied for more than one decade. They have been described explicitly in cases of type Ãn ( n ≥ 1 ) [13][9] and of rank ≤ 3 [1][4][10]. But there are only some partial results for an arbitrary irreducible affine Weyl group [2][7][8][16][17]. In [18], we constructed an algorithm to find a representative set of left cells of certain crystallographic group...
متن کاملThe Second Lowest Two-sided Cell in an Affine Weyl Group
Let Wa be an irreducible affine Weyl group with W0 the associated Weyl group. The present paper is to study the second lowest two-sided cell Ωqr of Wa. Let nqr be the number of left cells of Wa in Ωqr. We conjecture that the equality nqr = 1 2 |W0| should always hold. When Wa is either e An−1, n > 2, or of rank 6 4, this equality can be verified by the existing data (see 0.3). Then the main res...
متن کاملLOWER BOUNDARY HYPERPLANES OF THE CANONICAL LEFT CELLS IN THE AFFINE WEYL GROUP Wa( Ãn−1)
Let Γ be any canonical left cell of the affine Weyl group Wa of type e An−1, n > 1. We describe the lower boundary hyperplanes for Γ, which answer two questions of Humphreys. Let Wa be an affine Weyl group with Φ the root system of the corresponding Weyl group. Fix a positive root system Φ of Φ, there is a bijection from Wa to the set of alcoves in the euclidean space E spanned by Φ. We identif...
متن کاملThe Partial Order on Two-sided Cells of Certain Affine Weyl Groups
In their famous paper [6], Kazhdan and Lusztig introduced the concept of equivalence classes such as left cell, right cell and two-sided cell in a Coxeter group W . We inherit the notations 6 L , 6 R , 6 LR , ∼ L , ∼ R and ∼ LR in [6]. Thus w ∼ LR y (resp. w ∼ L y, resp. w ∼ R y) means that the elements w, y ∈ W are in the same two-sided cell (resp. left cell, resp. right cell) of W , etc. Conc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Australasian J. Combinatorics
دوره 56 شماره
صفحات -
تاریخ انتشار 2013