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Search: MSC category 20G99 ( None of the above, but in this section )

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1. CJM 2016 (vol 68 pp. 280)

da Silva, Genival; Kerr, Matt; Pearlstein, Gregory
Arithmetic of Degenerating Principal Variations of Hodge Structure: Examples Arising from Mirror Symmetry and Middle Convolution
We collect evidence in support of a conjecture of Griffiths, Green and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degenerations over a number field. After briefly summarizing how a result of Iritani implies this conjecture for a collection of hypergeometric Calabi-Yau threefold examples studied by Doran and Morgan, the authors investigate a sequence of (non-hypergeometric) examples in dimensions $1\leq d\leq6$ arising from Katz's theory of the middle convolution. A crucial role is played by the Mumford-Tate group (which is $G_{2}$) of the family of 6-folds, and the theory of boundary components of Mumford-Tate domains.

Keywords:variation of Hodge structure, limiting mixed Hodge structure, Calabi-Yau variety, middle convolution, Mumford-Tate group
Categories:14D07, 14M17, 17B45, 20G99, 32M10, 32G20

2. CJM 1999 (vol 51 pp. 1194)

Lusztig, G.
Subregular Nilpotent Elements and Bases in $K$-Theory
In this paper we describe a canonical basis for the equivariant $K$-theory (with respect to a $\bc^*$-action) of the variety of Borel subalgebras containing a subregular nilpotent element of a simple complex Lie algebra of type $D$ or~$E$.


3. CJM 1998 (vol 50 pp. 829)

Putcha, Mohan S.
Conjugacy classes and nilpotent variety of a reductive monoid
We continue in this paper our study of conjugacy classes of a reductive monoid $M$. The main theorems establish a strong connection with the Bruhat-Renner decomposition of $M$. We use our results to decompose the variety $M_{\nil}$ of nilpotent elements of $M$ into irreducible components. We also identify a class of nilpotent elements that we call standard and prove that the number of conjugacy classes of standard nilpotent elements is always finite.

Categories:20G99, 20M10, 14M99, 20F55

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