A tableau approach to the representation theory of 0-Hecke algebras

A Uniform Generalization of Some Combinatorial Hopf Algebras

“…In our earlier work [12] we obtained partial results on these characteristic maps using a tableau approach to the representation theory of 0-Hecke algebras; now we are able to get more complete results on them.…”

“…The coproduct of NSym is defined by ∆h k = k i=0 h i ⊗ h k−i , where h 0 := 1. A more explicit coproduct formula was provided in our earlier work [12].…”

“…Noncommutative symmetric functions of Type B. In our earlier work [12] we defined a type B analogue NSym B of NSym with two free Z-bases {h B α } and {s B α }, where α runs through all pseudo-compositions. If α = (α 1 , .…”

“…We call τ (type B) semistandard if each row is weakly increasing from left to right and each column is strictly increasing from top to bottom, including the extra 0. We showed in [12] that s B α is the sum of x w(τ ) for all semistandard tableaux τ of pseudo-ribbon shape α.…”

“…Let s D α be the sum of x w(τ ) for all type D semistandard tableaux τ of pseudo-ribbon shape α and define h D α := β α s D β . In our earlier work [12] we defined a type D analogue NSym D of NSym, which has two free Z-bases consisting of s D α and h D α , respectively, for all α |= D n and all n ≥ 2. We showed…”