Minuscule alcoves for GLn and GSp2n

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Nearby Cycles for Local Models of Some Shimura Varieties (2001, unknown): “The precise description of the sets ~ Wðn Þ is a difficult combinatorial problem (see [13] for the case nþ 1⁄4 1; n 1⁄4 0), but one can easily see that any w 2 ~ WðGSpð2dÞÞ is contained in some ~ Wðn Þ.”
Local models of Shimura varieties and a conjecture of Kottwitz (2011, background): “3 was first suggested by Kottwitz and Rapoport in [37].”
Alcoves associated to special fibers of local models (2001, methodology): “According to [15] and [11], the Bruhat order of Waff(Cn) is inherited from Waff(A2n).”
Local models of Shimura varieties, I. Geometry and combinatorics (2010, methodology): “ all i, the sum of the entries of the vector w! i ! iis r. Note that and all its Weyl conjugates, regarded as translation elements in fW, trivially satisfy (10) and (20). The main result for GL n in [KR] is that the set of all w2Wfsatisfying (10) and (20) is precisely the set Adm(fg), where the Bruh”
Stratifications in the reduction of Shimura varieties (2015, methodology): “That the strata are enumerated by Adm({μ})K is a consequence of the equality, proved in [29], between Adm({μ})K and Perm({μ})K (the μ-permissible set), cf.”