Author: Irina D. Suprunenko
Publisher: American Mathematical Soc.
ISBN: 0821843699
Category : Mathematics
Languages : en
Pages : 168
Book Description
The minimal polynomials of the images of unipotent elements in irreducible rational representations of the classical algebraic groups over fields of odd characteristic are found. These polynomials have the form $(t-1)^d$ and hence are completely determined by their degrees. In positive characteristic the degree of such polynomial cannot exceed the order of a relevant element. It occurs that for each unipotent element the degree of its minimal polynomial in an irreducible representation is equal to the order of this element provided the highest weight of the representation is large enough with respect to the ground field characteristic. On the other hand, classes of unipotent elements for which in every nontrivial representation the degree of the minimal polynomial is equal to the order of the element are indicated. In the general case the problem of computing the minimal polynomial of the image of a given element of order $p^s$ in a fixed irreducible representation of a classical group over a field of characteristic $p>2$ can be reduced to a similar problem for certain $s$ unipotent elements and a certain irreducible representation of some semisimple group over the field of complex numbers. For the latter problem an explicit algorithm is given. Results of explicit computations for groups of small ranks are contained in Tables I-XII. The article may be regarded as a contribution to the programme of extending the fundamental results of Hall and Higman (1956) on the minimal polynomials from $p$-solvable linear groups to semisimple groups.
The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic
Author: Irina D. Suprunenko
Publisher: American Mathematical Soc.
ISBN: 0821843699
Category : Mathematics
Languages : en
Pages : 168
Book Description
The minimal polynomials of the images of unipotent elements in irreducible rational representations of the classical algebraic groups over fields of odd characteristic are found. These polynomials have the form $(t-1)^d$ and hence are completely determined by their degrees. In positive characteristic the degree of such polynomial cannot exceed the order of a relevant element. It occurs that for each unipotent element the degree of its minimal polynomial in an irreducible representation is equal to the order of this element provided the highest weight of the representation is large enough with respect to the ground field characteristic. On the other hand, classes of unipotent elements for which in every nontrivial representation the degree of the minimal polynomial is equal to the order of the element are indicated. In the general case the problem of computing the minimal polynomial of the image of a given element of order $p^s$ in a fixed irreducible representation of a classical group over a field of characteristic $p>2$ can be reduced to a similar problem for certain $s$ unipotent elements and a certain irreducible representation of some semisimple group over the field of complex numbers. For the latter problem an explicit algorithm is given. Results of explicit computations for groups of small ranks are contained in Tables I-XII. The article may be regarded as a contribution to the programme of extending the fundamental results of Hall and Higman (1956) on the minimal polynomials from $p$-solvable linear groups to semisimple groups.
Publisher: American Mathematical Soc.
ISBN: 0821843699
Category : Mathematics
Languages : en
Pages : 168
Book Description
The minimal polynomials of the images of unipotent elements in irreducible rational representations of the classical algebraic groups over fields of odd characteristic are found. These polynomials have the form $(t-1)^d$ and hence are completely determined by their degrees. In positive characteristic the degree of such polynomial cannot exceed the order of a relevant element. It occurs that for each unipotent element the degree of its minimal polynomial in an irreducible representation is equal to the order of this element provided the highest weight of the representation is large enough with respect to the ground field characteristic. On the other hand, classes of unipotent elements for which in every nontrivial representation the degree of the minimal polynomial is equal to the order of the element are indicated. In the general case the problem of computing the minimal polynomial of the image of a given element of order $p^s$ in a fixed irreducible representation of a classical group over a field of characteristic $p>2$ can be reduced to a similar problem for certain $s$ unipotent elements and a certain irreducible representation of some semisimple group over the field of complex numbers. For the latter problem an explicit algorithm is given. Results of explicit computations for groups of small ranks are contained in Tables I-XII. The article may be regarded as a contribution to the programme of extending the fundamental results of Hall and Higman (1956) on the minimal polynomials from $p$-solvable linear groups to semisimple groups.
Bulletin
Author:
Publisher:
ISBN:
Category : Agriculture
Languages : en
Pages : 560
Book Description
Publisher:
ISBN:
Category : Agriculture
Languages : en
Pages : 560
Book Description
The Monthly Army List
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 1110
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 1110
Book Description
The army list
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 1242
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 1242
Book Description
The Monthly Army List
Author: Great Britain. Army
Publisher:
ISBN:
Category : Retired military personnel
Languages : en
Pages : 1166
Book Description
Publisher:
ISBN:
Category : Retired military personnel
Languages : en
Pages : 1166
Book Description
Chemical Modelling
Author: Professor Michael Springborg
Publisher: Royal Society of Chemistry
ISBN: 1839161701
Category : Science
Languages : en
Pages : 196
Book Description
Chemical modelling covers a wide range of disciplines and this book is the first stop for any materials scientist, biochemist, chemist or molecular physicist wishing to acquaint themselves with major developments in the applications and theory of chemical modelling. Containing both comprehensive and critical reviews, it is a convenient reference to the current literature. Coverage includes, but is not limited to, isomerism in polyoxometalate chemistry, modelling molecular magnets, molecular modelling of cyclodextrin inclusion complexes and graphene nanoribbons heterojunctions.
Publisher: Royal Society of Chemistry
ISBN: 1839161701
Category : Science
Languages : en
Pages : 196
Book Description
Chemical modelling covers a wide range of disciplines and this book is the first stop for any materials scientist, biochemist, chemist or molecular physicist wishing to acquaint themselves with major developments in the applications and theory of chemical modelling. Containing both comprehensive and critical reviews, it is a convenient reference to the current literature. Coverage includes, but is not limited to, isomerism in polyoxometalate chemistry, modelling molecular magnets, molecular modelling of cyclodextrin inclusion complexes and graphene nanoribbons heterojunctions.
Astronomical Observations
Author: Royal Observatory, Greenwich
Publisher:
ISBN:
Category : Astronomy
Languages : en
Pages : 1572
Book Description
Vols. for 1841-1914 include Rates of box and pocket chronometers on trial for purchase by the Board of Admiralty (varies slightly); 1888-1914 include Rates of chronometer watches on trial for purchase by the Board of Admiralty (varies slightly); 1838, 1845- include Reports of the Astronomer Royal to the Board of Visitors (these titles also issued separately).
Publisher:
ISBN:
Category : Astronomy
Languages : en
Pages : 1572
Book Description
Vols. for 1841-1914 include Rates of box and pocket chronometers on trial for purchase by the Board of Admiralty (varies slightly); 1888-1914 include Rates of chronometer watches on trial for purchase by the Board of Admiralty (varies slightly); 1838, 1845- include Reports of the Astronomer Royal to the Board of Visitors (these titles also issued separately).
Report No. FHWA-RD.
Author: United States. Federal Highway Administration. Offices of Research and Development
Publisher:
ISBN:
Category :
Languages : en
Pages : 296
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 296
Book Description
Lectures on the Theory of Functions of Real Variables: Rational numbers
Author: James Pierpont
Publisher:
ISBN:
Category : Functions of real variables
Languages : en
Pages : 584
Book Description
Publisher:
ISBN:
Category : Functions of real variables
Languages : en
Pages : 584
Book Description
Martingales in Banach Spaces
Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 1316679462
Category : Mathematics
Languages : en
Pages : 591
Book Description
This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this self-contained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses.
Publisher: Cambridge University Press
ISBN: 1316679462
Category : Mathematics
Languages : en
Pages : 591
Book Description
This book focuses on the major applications of martingales to the geometry of Banach spaces, and a substantial discussion of harmonic analysis in Banach space valued Hardy spaces is also presented. It covers exciting links between super-reflexivity and some metric spaces related to computer science, as well as an outline of the recently developed theory of non-commutative martingales, which has natural connections with quantum physics and quantum information theory. Requiring few prerequisites and providing fully detailed proofs for the main results, this self-contained study is accessible to graduate students with a basic knowledge of real and complex analysis and functional analysis. Chapters can be read independently, with each building from the introductory notes, and the diversity of topics included also means this book can serve as the basis for a variety of graduate courses.