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A098705 Coefficients in a certain Poincare series. +0
4
1, 1, 0, 0, 1, 2, 2, 2, 4, 7, 9, 12, 20, 32, 45, 66, 105, 164, 246, 372, 582, 909, 1393, 2146, 3355, 5240, 8132, 12660, 19825, 31051, 48554, 76038, 119409, 187635, 294760, 463520, 729980, 1150296, 1813100, 2859948, 4515225, 7132412 (list; graph; listen)
OFFSET

0,6

COMMENT

Let V=Sum_{k=1..infty} V_k be the graded vector space H_*(PC^infty)[1], which has Poincare series p(t)=t/(1-t^2). Let L be the free graded Lie algebra V. There is a graded involution theta on V induced by an involution on PC^infty, which acts on V_{2k+1} as (-1)^k. The sequence gives the dimensions of the +1-eigenspaces of theta on the graded components of L.

Lehrer-Segal give a recurrence; both this reference and the Lehrer article give the first 50 terms.

REFERENCES

G. I. Lehrer and G. B. Segal, Homology stability for classical regular semisimple varieties, Math. Zeit., 236 (2001), 251-290; p. 285.

LINKS

G. I. Lehrer, Some sequences arising at the interface of representation theory and homotopy theory

CROSSREFS

Sequence in context: A063823 A005865 A153988 this_sequence A029866 A161421 A077943

Adjacent sequences: A098702 A098703 A098704 this_sequence A098706 A098707 A098708

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Oct 28 2004

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Last modified December 21 10:15 EST 2009. Contains 171081 sequences.


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