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2.
In this paper we examine the automorphisms of GL 2(R) where R is a commutative ring having “many units”. As a corollary we classify the automorphisms when R is a local ring having 2 a unit and residue class field not the field of 3 elements. 相似文献
3.
The purpose of this paper is to describe an algorithm for computing weight multiplicities in a simple module of an algebraic Chevalley group over a field of positive characteristic p. The method is essentially more efficient than the one introduced by N. Burgoyne in 1971, especially when p is small. A concrete application is outlined where G is of type G
2 and p=5. 相似文献
9.
The properties of continued fractions, generalized golden sections, and generalized Fibonacci and Lucas numbers are proved on the ground of the properties of subsemigroups of the group of invertible integer matrices. Some properties of special recurrent sequences are studied. A new proof of the Pisot-Vijayaraghavan theorem is given. Some connections between continued fractions and Pisot numbers are considered. Some unsolved problems are stated. 相似文献
10.
The notion of a period of a cusp form on GL(2,D(??)), with respect to the diagonal subgroup D(??) X × D(??) X, is defined. Here D is a simple algebra over a global field F with a ring ?? of adeles. For D x = GL(1), the period is the value at 1/2 of the L-function of the cusp form on GL(2, ??). A cuspidal representation is called cyclic if it contains a cusp form with a non zero period. It is investigated whether the notion of cyclicity is preserved under the Deligne - Kazhdan correspondence, relating cuspidal representations on the group and its split form, where D is a matrix algebra. A local analogue is studied too, using the global technique. The method is based on a new bi-period summation formula. Local multiplicity one statements for spherical distributions, and non - vanishing properties of bi - characters, known only in a few cases, play a key role. 相似文献
11.
设U≥ 0 是量子群Uq(sl(2 ) )的非负部分 .在本文中 ,我们确定了U≥ 0 的中心Z(U≥ 0 )和U≥ 0 的所有不可约表示 相似文献
12.
Let be the classifying space of a finite group . Given a multiplicative cohomology theory , the assignment is a functor from groups to rings, endowed with induction (transfer) maps. In this paper we investigate these functors for complex oriented cohomology theories , using the theory of complex representations of finite groups as a model for what one would like to know. An analogue of Artin's Theorem is proved for all complex oriented : the abelian subgroups of serve as a detecting family for , modulo torsion dividing the order of . When is a complete local ring, with residue field of characteristic and associated formal group of height , we construct a character ring of class functions that computes . The domain of the characters is , the set of -tuples of elements in each of which has order a power of . A formula for induction is also found. The ideas we use are related to the Lubin-Tate theory of formal groups. The construction applies to many cohomology theories of current interest: completed versions of elliptic cohomology, -theory, etc. The th Morava K-theory Euler characteristic for is computed to be the number of -orbits in . For various groups , including all symmetric groups, we prove that is concentrated in even degrees. Our results about extend to theorems about , where is a finite -CW complex. 相似文献
13.
We determine the 2-modular character table of the Fischer group Fi 23. 相似文献
14.
A method for constructing special nonunitary representations of semisimple Lie groups by using representations of Iwasawa subgroups is suggested. As a typical example, the group U(2, 2) is studied. 相似文献
17.
We provide an explicit Plancherel formula for the p-adic group GL( n). We determine explicitly the Bernstein decomposition of Plancherel measure, including all numerical constants. We also prove a transfer-of-measure formula for GL( n). To cite this article: A.-M. Aubert, R. Plymen, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
18.
设U≥0是量子群Uq(sl(2))的非负部分,在本中,我们确定了U≥0的中心Z(U≥0)和U≥0有不可约表示。 相似文献
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