The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic PDF full book. Access full book title The Minimal Polynomials of Unipotent Elements in Irreducible Representations of the Classical Groups in Odd Characteristic by Irina D. Suprunenko. Download full books in PDF and EPUB format.
Author: Irina D. Suprunenko
Publisher: American Mathematical Society(RI)
ISBN: 9781470405533
Category : MATHEMATICS
Languages : en
Pages : 168
Get Book Here
Book Description
Author: Irina D. Suprunenko
Publisher: American Mathematical Society(RI)
ISBN: 9781470405533
Category : MATHEMATICS
Languages : en
Pages : 168
Get Book Here
Book Description
Author: Irina D. Suprunenko
Publisher: American Mathematical Soc.
ISBN: 082186680X
Category : Mathematics
Languages : en
Pages : 169
Get Book Here
Book Description
Author: Irina D. Suprunenko
Publisher: American Mathematical Soc.
ISBN: 0821843699
Category : Mathematics
Languages : en
Pages : 168
Get Book Here
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.
Author: Irina D. Suprunenko
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
Get Book Here
Book Description
Author: Ross Lawther
Publisher: American Mathematical Soc.
ISBN: 0821847694
Category : Mathematics
Languages : en
Pages : 201
Get Book Here
Book Description
Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.
Author: Ping-Shun Chan
Publisher: American Mathematical Soc.
ISBN: 0821848224
Category : Mathematics
Languages : en
Pages : 185
Get Book Here
Book Description
"Volume 204, number 957 (first of 5 numbers)."
Author: Tobias H. Jger
Publisher: American Mathematical Soc.
ISBN: 082184427X
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
The author proposes a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism, and its implementation in different models, is first discussed on an heuristic level and by means of simulations. In the considered examples, a stable and an unstable invariant circle undergo a saddle-node bifurcation, but instead of a neutral invariant curve there exists a strange non-chaotic attractor-repeller pair at the bifurcation point. This process is accompanied by a very characteristic behaviour of the invariant curves prior to their collision, which the author calls `exponential evolution of peaks'.
Author: Ralph Greenberg
Publisher: American Mathematical Soc.
ISBN: 082184931X
Category : Mathematics
Languages : en
Pages : 198
Get Book Here
Book Description
This paper shows that properties of projective modules over a group ring $\mathbf{Z}_p[\Delta]$, where $\Delta$ is a finite Galois group, can be used to study the behavior of certain invariants which occur naturally in Iwasawa theory for an elliptic curve $E$. Modular representation theory for the group $\Delta$ plays a crucial role in this study. It is necessary to make a certain assumption about the vanishing of a $\mu$-invariant. The author then studies $\lambda$-invariants $\lambda_E(\sigma)$, where $\sigma$ varies over the absolutely irreducible representations of $\Delta$. He shows that there are non-trivial relationships between these invariants under certain hypotheses.
Author: Skip Garibaldi
Publisher: American Mathematical Soc.
ISBN: 0821844040
Category : Mathematics
Languages : en
Pages : 102
Get Book Here
Book Description
This volume concerns invariants of $G$-torsors with values in mod $p$ Galois cohomology--in the sense of Serre's lectures in the book Cohomological invariants in Galois cohomology--for various simple algebraic groups $G$ and primes $p$. The author determines the invariants for the exceptional groups $F_4$ mod 3, simply connected $E_6$ mod 3, $E_7$ mod 3, and $E_8$ mod 5. He also determines the invariants of $\mathrm{Spin}_n$ mod 2 for $n \leq 12$ and constructs some invariants of $\mathrm{Spin}_{14}$. Along the way, the author proves that certain maps in nonabelian cohomology are surjective. These surjectivities give as corollaries Pfister's results on 10- and 12-dimensional quadratic forms and Rost's theorem on 14-dimensional quadratic forms. This material on quadratic forms and invariants of $\mathrm{Spin}_n$ is based on unpublished work of Markus Rost. An appendix by Detlev Hoffmann proves a generalization of the Common Slot Theorem for 2-Pfister quadratic forms.
Author: Adam Coffman
Publisher: American Mathematical Soc.
ISBN: 0821846574
Category : Mathematics
Languages : en
Pages : 105
Get Book Here
Book Description
"Volume 205, number 962 (first of 5 numbers)."
