Quiver varieties and Kashiwara's crystal <script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=default"> </script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\(","\)"]] }, TeX: { extensions: ["AMSmath.js", "AMSsymbols.js"], Macros: { CC: "{\\mathbb C}", C: "{\\mathbb C}", R: "{\\mathbb R}", Q: "{\\mathbb Q}", Z: "{\\mathbb Z}", cO: "{\\mathcal O}", diag: "\\mathop{\\mathrm{diag}}\\nolimits", np: "[{#1}#2{#1}, 2]", operatorname: ["\\mathrm{#1}",1], } } }); </script> <script type="text/javascript" src="MyConfig.js"> </script> <meta http-equiv="X-UA-Compatible" CONTENT="IE=EmulateIE7" /> </head> <body bgcolor= "#90C0C0"> <center> <h1>Quiver varieties and Kashiwara's crystal </center> <center> Hiraku Nakajima (Kyoto) </center> Abstract : This is an introductory lecture series on an approach to Kashiwara's crystal via quiver varieties. I will explain <ol> <li> Definition of quiver varieties and their lagrangian subvarieties <li> Definition of Kashiwara operators on the set of irreducible components of the lagrangian subvarieties <li> Tensor products of crystals and their realization via quiver varieties <li> Some explicit parametrization of lagrangian subvarieties </ol> <hr> <address> <a href="mailto:nakajima@math.kyoto-u.ac.jp">nakajima@math.kyoto-u.ac.jp</a> </address>