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Web page: Alexandru I. Suciu | Created: May 25, 2001 |
| Maintained by: Misha Kogan | URL: http://www.math.neu.edu/~GASC/gas/sottile01.html |
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| Virtual crystals |
| Abstract: Crystal bases were introduced by Kashiwara
in the early 90's. They are bases of representations of the quantized universal
enveloping algebra $U_q(g)$ as q tends to zero. There are two main categories
of crystals when $g$ is an affine Kac-Moody algebra:
(1) crystal bases of infinite-dimensional integrable highest weight $U_q(g)$-modules and (2) crystal bases of finite-dimensional $U'_q(g)$-modules. Whereas much is known about the first category, the second category of crystals is still far from well-understood. In this talk I will give an introduction to affine crystals and explain how virtual crystals can provide more information about the second category of affine crystals. Virtual crystals are obtained by extending certain embeddings of classical crystals to the affine case. This talk is based on joint work with M. Okado and M. Shimozono (math.QA/0105017). |
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Web page: Alexandru I. Suciu | Created: May 25, 2001 |
| Maintained by: Misha Kogan | URL: http://www.math.neu.edu/~GASC/gas/sottile01.html |