Regular characters of groups of type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msub><mml:mrow><mml:mi mathvariant="sans-serif">A</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub></mml:math> over discrete valuation rings

Krakovski, Roi; Onn, Uri; Singla, Pooja

doi:10.1016/j.jalgebra.2017.10.018

Cited by 15 publications

(26 citation statements)

References 17 publications

(15 reference statements)

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“…Takase conjectured that for

p = char {double-struckF}_{q}

large enough, this element is trivial (see [, Conjecture 4.6.5]). Using our main result, we deduce a strong form of Takase's conjecture, valid for any prime

p

(this is also proved, for

p \neq 2

, in ). Corollary Suppose

β \in {frakturg}_{r}

is regular.…”

Section: Discussionsupporting

confidence: 56%

“…this element is trivial (see [23,Conjecture 4.6.5]). Using our main result, we deduce a strong form of Takase's conjecture, valid for any prime p (this is also proved, for p = 2, in [12]).…”

Section: Construction Of Regular Representationssupporting

confidence: 57%

“…In [12] the dimensions and multiplicities of the regular representations of GL N (o r ) were determined for p = 2. This can also be done using Theorem 4.10, and our construction implies that the dimension and multiplicity formulas there remain valid for p = 2.…”

Section: Construction Of Regular Representationsmentioning

confidence: 99%

“…However, it was noted by Takase that the results in do not give all the split regular representations, and in any case, there exist many non‐split non‐cuspidal regular representations. While the present work was in preparation, Krakovski, Onn and Singla gave a construction of the regular representations of

G_{r}

when the residue characteristic

p

is not 2. In the present paper we complete the picture by giving a construction of all the regular representations of

G_{r}

.…”

Section: Introductionmentioning

confidence: 99%

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The regular representations of GLN over finite local principal ideal rings

Stasinski

Stevens

2017

Bull. London Math. Soc.

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Abstract. Let o be the ring of integers in a non-Archimedean local field with finite residue field, p its maximal ideal, and r ≥ 2 an integer. An irreducible representation of the finite group Gr = GL N (o/p r ) is called regular if its restriction to the principal congruence kernel K r−1 = 1 + p r−1 M N (o/p r ) consists of representations whose stabilisers modulo K 1 are centralisers of regular elements in M N (o/p).The regular representations form the largest class of representations of Gr which is currently amenable to explicit construction. Their study, motivated by constructions of supercuspidal representations, goes back to Shintani, but the general case remained open for a long time. In this paper we give an explicit construction of all the regular representations of Gr.

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“…Takase conjectured that for

p = char {double-struckF}_{q}

large enough, this element is trivial (see [, Conjecture 4.6.5]). Using our main result, we deduce a strong form of Takase's conjecture, valid for any prime

p

(this is also proved, for

p \neq 2

, in ). Corollary Suppose

β \in {frakturg}_{r}

is regular.…”

Section: Discussionsupporting

confidence: 56%

Section: Construction Of Regular Representationssupporting

confidence: 57%

Section: Construction Of Regular Representationsmentioning

confidence: 99%

G_{r}

when the residue characteristic

p

is not 2. In the present paper we complete the picture by giving a construction of all the regular representations of

G_{r}

.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The regular representations of GLN over finite local principal ideal rings

Stasinski

Stevens

2017

Bull. London Math. Soc.

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“…For the sake of brevity, rather then rehashing the proof appearing in great detail in loc. cit., our focus for the remainder of this section would be on setting up the necessary preliminaries and state the necessary modification required in order to adapt the construction of [22] to the current setting.…”

mentioning

confidence: 99%

Regular characters of classical groups over complete discrete valuation rings

Shechter

2019

Journal of Pure and Applied Algebra

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Let o be a complete discrete valuation ring with finite residue field k of odd characteristic, and let G be a symplectic or special orthogonal group scheme over o. For any ℓ ∈ N let G ℓ denote the ℓ-th principal congruence subgroup of G(o). An irreducible character of the group G(o) is said to be regular if it is trivial on a subgroup G ℓ+1 for some ℓ, and if its restriction to G ℓ /G ℓ+1 ≃ Lie(G)(k) consists of characters of minimal G(k alg )-stabilizer dimension . In the present paper we consider the regular characters of such classical groups over o, and construct and enumerate all regular characters of G(o), when the characteristic of k is greater than two. As a result, we compute the regular part of their representation zeta function.

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Flags and orbits of connected reductive groups over local rings

Chen

2019

Math. Ann.

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We prove that generic higher Deligne-Lusztig representations over truncated formal power series are non-nilpotent, when the parameters are non-trivial on the biggest reduction kernel of the centre; we also establish a relation between the orbits of higher Deligne-Lusztig representations of SL n and of GL n . Then we introduce a combinatorial analogue of Deligne-Lusztig construction for general and special linear groups over local rings; this construction generalises the higher Deligne-Lusztig representations and affords all the nilpotent orbit representations, and for GL n it also affords all the regular orbit representations as well as the invariant characters of the Lie algebra.

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Regular characters of groups of type An over discrete valuation rings

Cited by 15 publications

References 17 publications

The regular representations of GLN over finite local principal ideal rings

The regular representations of GLN over finite local principal ideal rings

Regular characters of classical groups over complete discrete valuation rings

Flags and orbits of connected reductive groups over local rings

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