On Kostant sections and topological nilpotence

Adler, Jeffrey D.; Fintzen, Jessica; Varma, Sandeep

doi:10.1112/jlms.12106

Cited by 3 publications

(9 citation statements)

References 32 publications

(90 reference statements)

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“…If G is of type A n−1 , then |Z| divides h = n. If divides n, then q n/ ≡ q n ≡ 1 mod , contradicting the order of q. Similar arguments work for type 2 A n (n ≥ 2). Proof.…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 77%

“…If h/t is odd, then T (f) has no conjugate self-dual characters in general position. Moreover, suppose that G does not have type 2 (2). Then the following hold:…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 99%

“…In this case, a generator of L is a conjugate self-dual element in general position. Now suppose that h = 2 and (q, h) = (2,6). Then by [4, Theorem V], there exists a prime such that the multiplicative order of q mod is h. Let ch w denote the characteristic polynomial of the action of w on X, and let r denote the rank of X.…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 99%

“…It remains to handle the cases where (q, h) = (2,6). From [13, §3.18, Table 2] and [19,Table 10,page 184], G has one of the following types:…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 99%

“…Lemma 2.3. Let G and be as in Proposition 2.2, and let Z denote the center of G. Assume that h = 2 and (q, h) = (2,6). Then is coprime to |Z|.…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 99%

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Self-dual cuspidal representations

Adler¹,

Mishra²

2020

Represent. Theory

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Let G G be a connected reductive group over a finite field f \mathfrak {f} of order q q . When q ≤ 5 q\leq 5 , we make further assumptions on G G . Then we determine precisely when G ( f ) G(\mathfrak {f}) admits irreducible, cuspidal representations that are self-dual, of Deligne-Lusztig type, or both. Finally, we outline some consequences for the existence of self-dual supercuspidal representations of reductive p p -adic groups.

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“…If G is of type A n−1 , then |Z| divides h = n. If divides n, then q n/ ≡ q n ≡ 1 mod , contradicting the order of q. Similar arguments work for type 2 A n (n ≥ 2). Proof.…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 77%

“…If h/t is odd, then T (f) has no conjugate self-dual characters in general position. Moreover, suppose that G does not have type 2 (2). Then the following hold:…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 99%

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 99%

“…It remains to handle the cases where (q, h) = (2,6). From [13, §3.18, Table 2] and [19,Table 10,page 184], G has one of the following types:…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 99%

“…Lemma 2.3. Let G and be as in Proposition 2.2, and let Z denote the center of G. Assume that h = 2 and (q, h) = (2,6). Then is coprime to |Z|.…”

Section: Proposition 22 Suppose That G Is Absolutely Almost Simple T Is the Degree Of The Splitting Field Of G T Is The Coxeter Torus In mentioning

confidence: 99%

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Self-dual cuspidal representations

Adler¹,

Mishra²

2020

Represent. Theory

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The companion section for classical groups

Hameister,

Ngô

2024

Int. J. Math.

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We use the companion matrix construction for [Formula: see text] to build canonical sections of the Chevalley map [Formula: see text] for classical groups [Formula: see text] as well as the group [Formula: see text]. To do so, we construct canonical tensors on the associated spectral covers. As an application, we make explicit lattice descriptions of affine Springer fibers and Hitchin fibers for classical groups and [Formula: see text].

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Torsors on loop groups and the Hitchin fibration

Bouthier¹,

Česnavičius²

2019

Preprint

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In his proof of the fundamental lemma, Ngô established the product formula for the Hitchin fibration over the anisotropic locus. One expects this formula over the larger generically regular semisimple locus, and we confirm this by deducing the relevant vanishing statement for torsors over loop groups Rpptqq from a general formula for PicpRpptqqq. In the build up to the product formula, we present general algebraization, approximation, and invariance under Henselian pairs results for torsors, give short new proofs for the Elkik approximation theorem and the Chevalley isomorphism g G -t{W , and improve results on the geometry of the Chevalley morphism g Ñ g G.

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On Kostant sections and topological nilpotence

Cited by 3 publications

References 32 publications

Self-dual cuspidal representations

Self-dual cuspidal representations

The companion section for classical groups

Torsors on loop groups and the Hitchin fibration

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