Abelian subalgebras in Z_2-graded Lie algebras and affine Weyl groups

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Let g=g_0+ g_1 be a simple Z_2-graded Lie algebra and let b_0 be a fixed Borel subalgebra of g_0. We describe and enumerate the abelian b_0-stable subalgebras of g_1.
21 pages, amstex file. Minor corrections. Introduction slightly expanded. To appear in IMRN

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