| Title:
|
On the combinatorics of Kac's asymmetry function (English) |
| Author:
|
Green, R. M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
217-235 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We use categories to recast the combinatorial theory of full heaps, which are certain labelled partially ordered sets that we introduced in previous work. This gives rise to a far simpler set of definitions, which we use to outline a combinatorial construction of the so-called loop algebras associated to affine untwisted Kac--Moody algebras. The finite convex subsets of full heaps are equipped with a statistic called parity, and this naturally gives rise to Kac's asymmetry function. The latter is a key ingredient in understanding the (integer) structure constants of simple Lie algebras with respect to certain Chevalley bases, which also arise naturally in the context of heaps. (English) |
| Keyword:
|
Lie algebra |
| Keyword:
|
Chevalley basis |
| Keyword:
|
heap |
| MSC:
|
06A07 |
| MSC:
|
17B20 |
| MSC:
|
17B67 |
| idZBL:
|
Zbl 1224.17032 |
| idMR:
|
MR2682475 |
| . |
| Date available:
|
2010-05-21T12:46:03Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140101 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
