The combinatorics of Bernstein functions

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Introduction to Shimura Varieties with Bad Reduction of Parahoric Type (2004, methodology): “¯ η : V ⊗ Apf ∼= H1 (A, A p f) mod K p that respects the bilinear forms on both sides up to a scalar in (Apf) × , and”
Nearby Cycles for Local Models of Some Shimura Varieties (2001, unknown): “It can be deduced easily, see [7], from results of Lusztig [12] and Kato [10].”
Local models of Shimura varieties, I. Geometry and combinatorics (2010, methodology): “Then in (i), we have Admf ({µ}) = Permf ({µ}) for any {µ} and any f when R involves only type A; this was proved in the case of minuscule {µ} in [KR, 9.6], and the general case is an immediate consequence of Görtz’s result [Gö4, Cor. 9] (which itself makes crucial use of the cited result in the Iw”
Pro-p-Iwahori Hecke ring and supersingular -representations (2005, unknown): “a) Haines [3] lemma 5.”