The symplectic group and determinants
نویسندگان
چکیده
منابع مشابه
Lagrangian spheres, symplectic surfaces and the symplectic mapping class group
Given a Lagrangian sphere in a symplectic 4-manifold (M,ω) with b+ = 1, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension κ of (M,ω) is −∞, this minimal intersection property turns out to be very powerful for both the uniqueness and existence problems of Lagrangian spheres. On the uniqueness side, for a symplectic rational manifold and any class which is...
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We define a family of groups that include the mapping class group of a genus g surface with one boundary component and the integral symplectic group Sp.2g;Z/ . We then prove that these groups are finitely generated. These groups, which we call mapping class groups over graphs, are indexed over labeled simplicial graphs with 2g vertices. The mapping class group over the graph is defined to be ...
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we examine the symplectic group $sp_{2m}(q)$ and its correspondingaffine subgroup. we construct the affine subgroup and show that itis a split extension. as an illustration of the above we study theaffine subgroup $2^5{:}sp_4(2)$ of the group $sp_6(2)$.
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Let p be an odd prime. It is known that the symplectic group Sp2n(p) has two (algebraically conjugate) irreducible representations of degree (pn +1)/2 realized over Q(√ p), where = (−1)(p−1)/2. We study the integral lattices related to these representations for the case pn ≡ 1 mod 4. (The case pn ≡ 3 mod 4 has been considered in a previous paper.) We show that the class of invariant lattices co...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1980
ISSN: 0021-8693
DOI: 10.1016/0021-8693(80)90101-5