arXiv subjects

Lei Zhao

Publications and source records attributed to Lei Zhao.

255 records · Page 15Linked to original sources

arXiv2009

Zero-error feedback capacity via dynamic programming

In this paper, we study the zero-error capacity for finite state channels with feedback when channel state information is known to both the transmitter and the receiver. We prove that the zero-error capacity in this case can be obtained through the solution of a dynamic programming problem. Each iteration of the dynamic programming provides lower and upper bounds on the zero-error capacity, and in the limit, the lower bound coincides with the zero-error feedback capacity. Furthermore, a sufficient condition for solving the dynamic programming problem is provided through a fixed-point equation. Analytical solutions for several examples are provided.

cs.IT↗

arXiv2009

Typical blocks of Lie superalgebras in prime characteristic

For a type I basic classical Lie superalgebra $\mathfrak{g}=\mathfrak{g}_{\bar{0}} \oplus \mathfrak{g}_{\bar{1}}$, we establish an equivalence between typical blocks of categories of $U_χ(\mathfrak{g})$-modules and $U_χ(mathfrak{g}_{\bar{0})$-modules. We then deduce various consequences from the equivalence.

math.RT↗

arXiv2009

Representations of Lie Superalgebras in Prime Characteristic I

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a mixture of p-power and 2-power divisibilities of dimensions of modules. We establish the Conjecture for basic classical Lie superalgebras.

math.RT↗