On the Garsia Lie Idempotent
2005 ◽
Vol 48
(3)
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pp. 445-454
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Keyword(s):
AbstractThe orthogonal projection of the free associative algebra onto the free Lie algebra is afforded by an idempotent in the rational group algebra of the symmetric group Sn, in each homogenous degree n. We give various characterizations of this Lie idempotent and show that it is uniquely determined by a certain unit in the group algebra of Sn−1. The inverse of this unit, or, equivalently, the Gram matrix of the orthogonal projection, is described explicitly. We also show that the Garsia Lie idempotent is not constant on descent classes (in fact, not even on coplactic classes) in Sn.
2013 ◽
Vol 162
(5)
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pp. 965-1002
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Keyword(s):
1990 ◽
Vol 55
(1)
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pp. 93-129
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2003 ◽
Vol 75
(1)
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pp. 9-21
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Keyword(s):
1991 ◽
Vol 79
(1)
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pp. 227-239
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1993 ◽
Vol 119
(4)
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pp. 1029-1029
1994 ◽
Vol 341
(1)
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pp. 315-333
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