Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positivity conjectures for Kazhdan-Lusztig theory on twisted
  involutions: the universal case   Let $(W,S)$ be a Coxeter system and let $w \mapsto w^*$ be an involution of
$W$ which preserves the set of simple generators $S$. Lusztig and Vogan have
recently shown that the set of twisted involutions (i.e., elements $w \in W$
with $w^{-1} = w^*$) naturally generates a module of the Hecke algebra of
$(W,S)$ with two distinguished bases. The transition matrix between these bases
defines a family of polynomials $P^\sigma_{y,w}$ which one can view as
"twisted" analogues of the much-studied Kazhdan-Lusztig polynomials of $(W,S)$.
The polynomials $P^\sigma_{y,w}$ can have negative coefficients, but display
several conjectural positivity properties of interest. This paper reviews
Lusztig's construction and then proves three such positivity properties for
Coxeter systems which are universal (i.e., having no braids relations),
generalizing previous work of Dyer. Our methods are entirely combinatorial and
elementary, in contrast to the geometric arguments employed by Lusztig and
Vogan to prove similar positivity conjectures for crystallographic Coxeter
systems.

29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org