Varieties of pairs of nilpotent matrices annihilating each other
نویسندگان
چکیده
منابع مشابه
Jordan forms for mutually annihilating nilpotent pairs
We consider pairs of n × n commuting matrices over an algebraically closed field F . For n, a, b (all at least 2) let V(n, a, b) be the variety of all pairs (A,B) of commuting nilpotent matrices such that AB = BA = A = B = 0. In [14] Schröer classified the irreducible components of V(n, a, b) and thus answered a question stated by Kraft [9, p. 201] (see also [3] and [10]). If μ = (μ1, μ2, . . ....
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Let B be a nilpotent matrix and suppose that its Jordan canonical form is determined by a partition λ. Then it is known that its nilpotent commutator NB is an irreducible variety and that there is a unique partition μ such that the intersection of the orbit of nilpotent matrices corresponding to μ with NB is dense in NB. We prove that map D given by D(λ) = μ is an idempotent map. This answers a...
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Pairs (A,B) of mutually annihilating operators AB = BA = 0 on a finite dimensional vector space over an algebraically closed field were classified by Gelfand and Ponomarev [Russian Math. Surveys 23 (1968) 1–58] by method of linear relations. The classification of (A,B) over any field was derived by Nazarova, Roiter, Sergeichuk, and Bondarenko [J. Soviet Math. 3 (1975) 636–654] from the classifi...
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We determine which nilpotent orbits in E6 have closures which are normal varieties and which do not. At the same time we are able to verify a conjecture in [14] concerning functions on nonspecial nilpotent orbits for E6.
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Let n and q be given integers and X a finite set with n elements. The following theorem is proved for n > n0(q). The family of all q-element subsets of X can be partitioned into disjoint pairs (except possibly one if (n q ) is odd), so that |A1∩A2|+ |B1 ∩B2| ≤ q, |A1 ∩B2|+ |B1 ∩A2| ≤ q holds for any two such pairs {A1, B1} and {A2, B2}. This is a sharpening of a theorem in [2]. It is also shown...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2004
ISSN: 0010-2571,1420-8946
DOI: 10.1007/s00014-003-0788-3