A098705 Coefficients in a certain Poincaré series [or Poincare series].

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

Offset

0,6

Comments

Let V=Sum_{k=1..infty} V_k be the graded vector space H_*(PC^infty)[1], which has Poincaré series [or 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

Table of n, a(n) for n=0..41.

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

Crossrefs

Sequence in context: A245257 A153988 A253059 * A029866 A244458 A286613

Adjacent sequences: A098702 A098703 A098704 * A098706 A098707 A098708

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 28 2004

Status

approved