scholarly journals Reidemeister spectrum of special and general linear groups over some fields contains 1

2019 ◽  
Vol 18 (08) ◽  
pp. 1950153 ◽  
Author(s):  
Timur Nasybullov
Keyword(s):  
Transcendence Degree ◽  
General Linear ◽  
Linear Groups ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
General Linear Groups ◽  
Zero Characteristic ◽  
Field Automorphism

We prove that if [Formula: see text] is an algebraically closed field of zero characteristic which has infinite transcendence degree over [Formula: see text], then there exists a field automorphism [Formula: see text] of [Formula: see text] and [Formula: see text] such that [Formula: see text]. This fact implies that [Formula: see text] and [Formula: see text] do not possess the [Formula: see text]-property. However, if the transcendece degree of [Formula: see text] over [Formula: see text] is finite, then [Formula: see text] and [Formula: see text] are known to possess the [Formula: see text]-property [13].

scholarly journals general linear groups

1997 ◽  
Vol 90 (3) ◽  
pp. 549-576 ◽  
Author(s):  
Avner Ash ◽  
Mark McConnell
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
General Linear Groups

scholarly journals An algebraically closed field

1968 ◽  
Vol 9 (2) ◽  
pp. 146-151 ◽  
Author(s):  
F. J. Rayner
Keyword(s):  
Positive Integer ◽  
Power Series ◽  
Formal Power Series ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Zero Characteristic ◽  
Image Position ◽  
Formal Power ◽  
Puiseux Expansions

Letkbe any algebraically closed field, and denote byk((t)) the field of formal power series in one indeterminatetoverk. Letso thatKis the field of Puiseux expansions with coefficients ink(each element ofKis a formal power series intl/rfor some positive integerr). It is well-known thatKis algebraically closed if and only ifkis of characteristic zero [1, p. 61]. For examples relating to ramified extensions of fields with valuation [9, §6] it is useful to have a field analogous toKwhich is algebraically closed whenkhas non-zero characteristicp. In this paper, I prove that the setLof all formal power series of the form Σaitei(where (ei) is well-ordered,ei=mi|nprt,n∈ Ζ,mi∈ Ζ,ai∈k,ri∈ Ν) forms an algebraically closed field.

scholarly journals Restriction for general linear groups: The local non-tempered Gan–Gross–Prasad conjecture (non-Archimedean case)

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Kei Yuen Chan
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Branching Laws ◽  
General Linear Groups ◽  
Branching Law

Abstract We prove a local Gan–Gross–Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean fields. We also generalize to Bessel and Fourier–Jacobi models and study a possible generalization to Ext-branching laws.

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