scholarly journals Closure relations of Newton strata in Iwahori double cosets

2021 ◽  
Author(s):  
Stefania Trentin ◽  
Eva Viehmann
Keyword(s):  
Reductive Group ◽  
Double Cosets ◽  
Closure Relations ◽  
Newton Stratification

AbstractWe consider the Newton stratification on Iwahori double cosets for a connected reductive group. We prove the existence of Newton strata whose closures cannot be expressed as a union of strata, and show how this is implied by the existence of non-equidimensional affine Deligne–Lusztig varieties. We also give an explicit example for a group of type $$A_4$$ A 4 .

scholarly journals Generic Newton points and the Newton poset in Iwahori-double cosets

2020 ◽  
Vol 8 ◽  
Author(s):  
Elizabeth Milićević ◽  
Eva Viehmann
Keyword(s):  
Reductive Group ◽  
Loop Group ◽  
Index Set ◽  
Double Cosets ◽  
Large Classes ◽  
Bruhat Graph ◽  
Newton Stratification ◽  
Quantum Bruhat Graph

Abstract We consider the Newton stratification on Iwahori-double cosets in the loop group of a reductive group. We describe a group-theoretic condition on the generic Newton point, called cordiality, under which the Newton poset (that is, the index set for non-empty Newton strata) is saturated and Grothendieck’s conjecture on closures of the Newton strata holds. Finally, we give several large classes of Iwahori-double cosets for which this condition is satisfied by studying certain paths in the associated quantum Bruhat graph.

Regular Elliptic Classes and the Stable Relative Trace Formula

1992 ◽  
Vol 35 (2) ◽  
pp. 230-236
Author(s):  
K. F. Lai
Keyword(s):  
Number Field ◽  
Trace Formula ◽  
Algebraic Number ◽  
Reductive Group ◽  
Algebraic Number Field ◽  
Double Cosets ◽  
Relative Trace Formula

AbstractWe study the relative trace formula of a reductive group over an algebraic number field. Following Langlands we stabilize the geometric side of the relative trace formula contributed by the elliptic regular double cosets.

scholarly journals Minimal Newton Strata in Iwahori Double Cosets

2019 ◽  
Author(s):  
Eva Viehmann
Keyword(s):  
Finite Subset ◽  
Minimal Element ◽  
Reductive Group ◽  
Double Coset ◽  
Loop Group ◽  
Conjugacy Classes ◽  
Regularity Assumption ◽  
Double Cosets

Abstract The set of Newton strata in a given Iwahori double coset in the loop group of a reductive group $G$ is indexed by a finite subset of the set $B(G)$ of Frobenius-conjugacy classes. For unramified $G$, we show that it has a unique minimal element and determine this element. Under a regularity assumption, we also compute the dimension of the corresponding Newton stratum. We derive corresponding results for affine Deligne–Lusztig varieties.

scholarly journals CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY

2021 ◽  
Author(s):  
MÁTYÁS DOMOKOS ◽  
VESSELIN DRENSKY
Keyword(s):  
Lie Algebra ◽  
Associative Algebra ◽  
Invariant Theory ◽  
Reductive Group ◽  
Symmetric Tensor ◽  
Free Associative Algebra ◽  
Tensor Algebra ◽  
Enveloping Algebra ◽  
Finite Dimensional ◽  
Degree Bounds

AbstractThe problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.

scholarly journals Statistical Enumeration of Groups by Double Cosets

2021 ◽  
Author(s):  
Persi Diaconis ◽  
Mackenzie Simper
Keyword(s):  
Double Cosets

scholarly journals A decomposition formula for representations

1987 ◽  
Vol 107 ◽  
pp. 63-68 ◽  
Author(s):  
George Kempf
Keyword(s):  
Irreducible Representation ◽  
General Formula ◽  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Maximal Torus ◽  
Reductive Group ◽  
Irreducible Representations ◽  
Levi Subgroup ◽  
Know How ◽  
Decomposition Formula

Let H be the Levi subgroup of a parabolic subgroup of a split reductive group G. In characteristic zero, an irreducible representation V of G decomposes when restricted to H into a sum V = ⊕mαWα where the Wα’s are distinct irreducible representations of H. We will give a formula for the multiplicities mα. When H is the maximal torus, this formula is Weyl’s character formula. In theory one may deduce the general formula from Weyl’s result but I do not know how to do this.

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