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61.
Wolfgang Soergel 《Geometric And Functional Analysis》2008,17(6):2066-2089
On the space of homomorphisms from a Verma module to an indecomposable tilting module of the BGG-category we define a natural filtration following Andersen [A] and establish a formula expressing the dimensions of the filtration
steps in terms of coefficients of Kazhdan–Lusztig polynomials.
Received: May 2006, Revision: July 2007, Accepted: July 2007 相似文献
62.
Let n ≥ 1 be an integer and π a permutation of I = {1, ⋯ ,n}. For any ring R, we provide a systematic construction of rings A which contain R as a subring and enjoy the following properties: (a) 1 = ∑
i ∈ I
e
i
with the e
i
orthogonal idempotents; (b) e
i
x = xe
i
for all i ∈ I and x ∈ R; (c) e
i
A
e
j
≠ 0 for all i, j ∈ I; (d) e
i
A
A
≇ e
j
A
A
unless i = j; (e) every e
i
Ae
i
is a local ring whenever R is; (f) e
i
A
A
≅ Hom
R
(Ae
π(i),R
R
) and
A
Ae
π(i) ≅
A
Hom
R
(e
i
A,
R
R) for all i ∈ I; and (g) there exists a ring automorphism η ∈ Aut(A) such that η(e
i
) = e
π(i) for all i ∈ I. Furthermore, for any nonempty π-stable subset J of I, the mapping cone of the multiplication map is a tilting complex.
Dedicated to Takeshi Sumioka on the occasion of his 60th birthday. 相似文献