MarriageTheoremのこと

_ プレプリント確認状況：arXiv:math 1月4日分まで、arXiv:quant-ph 5月31日分まで、IACR ePrint：2012/130まで

_ ↑ついにarXiv:mathのチェック状況が2012年に追い付いた。感慨深い。

_ 気になった論文その１：Asymptotical behaviour of roots of infinite Coxeter groups I（Christophe Hohlweg, Jean-Philippe Labbé, Vivien Ripoll, arXiv:1112.5415v1）

Let W be an infinite Coxeter group. We initiate the study of the set E of limit points of "normalized" positive roots (representing the directions of the roots) of W. We show that E is contained in the isotropic cone of the bilinear form B associated to a geometric representation, and illustrate this property with numerous examples and pictures in rank 3 and 4. We also define a natural geometric action of W on E, and then we exhibit a countable subset of E, formed by limit points for the dihedral reflection subgroups of W. We explain that this subset can be built from the intersection with Q of the lines passing through two positive roots, and we establish that it is dense in E.

その２：Alternating subgroups of Coxeter groups and their spinor extensions（O. V. Ogievetsky, L. Poulain d'Andecy, arXiv:1112.6347v1）

Let $G$ be a discrete Coxeter group, $G^+$ its alternating subgroup and $\tilde{G}^+$ the spinor cover of $G^+$. A presentation of the groups $G^+$ and $\tilde{G}^+$ is proved for an arbitrary Coxeter system $(G,S)$; the generators are related to edges of the Coxeter graph. Results of the Coxeter--Todd algorithm - with this presentation - for the chains of alternating groups of types A, B and D are given.

分野にMathematical Physicsが入っているのが気になる。どんな応用がある話なんだろうか。

その３：On counterexamples in questions of unique determination of convex bodies（Dmitry Ryabogin, Vlad Yaskin, arXiv:1201.0544v1）

We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.

_ 昨日書いた3/14と.214の話を妻に話したら好評だった。ああいう話を面白がってくれる人でよかったなぁと思う。