Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Lusztig-Dupont homology of flag complexes   Let $V$ be an $n$-dimensional vector space over the finite field of order
$q$. The spherical building $X_V$ associated with $GL(V)$ is the order complex
of the nontrivial linear subspaces of $V$. Let $\mathfrak{g}$ be the local
coefficient system on $X_V$, whose value on the simplex $\sigma=[V_0 \subset
\cdots \subset V_p] \in X_V$ is given by $\mathfrak{g}(\sigma)=V_0$. Following
the work of Lusztig and Dupont, we study the homology module
$D^k(V)=\tilde{H}_{n-k-1}(X_V;\mathfrak{g})$. Our results include a
construction of an explicit basis of $D^1(V)$, and the following twisted
analogue of a result of Smith and Yoshiara: For any $1 \leq k \leq n-1$, the
minimal support size of a non-zero $(n-k-1)$-cycle in the twisted homology
$\tilde{H}_{n-k-1}(X_V;\wedge^k \mathfrak{g})$ is $\frac{(n-k+2)!}{2}$.

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The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc