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We show that the Kazhdan-Lusztig category KL_k of level-k finite-length modules with highest-weight composition factors for the affine Lie superalgebra gl(1|1)ˆ has vertex algebraic braided tensor supercategory structure, and that its full subcategory O_k^fin of objects with semisimple Cartan subalgebra actions is a tensor subcategory. We show that every simple gl(1|1)ˆ-module in KL_k has a projective cover in O_k^fin, and we determine all fusion rules involving simple and projective objects in O_k^fin. Then using Knizhnik-Zamolodchikov equations, we prove that KL_k and O_k^fin are rigid. As an application of the tensor supercategory structure on O_k^fin, we study certain module categories for the affine Lie superalgebra sl(2|1)ˆ at levels 1 and −1/2. In particular, we obtain a tensor category of sl(2|1)ˆ-modules at level −1/2 that includes relaxed highest-weight modules and their images under spectral flow.

3-D CAD models are an important digital resource in the manufacturing industry. 3-D CAD model retrieval has become a key technology in product lifecycle management enabling the reuse of existing design data. In this paper, we propose a new method to retrieve 3-D CAD models based on 2-D pen-based sketch inputs. Sketching is a common and convenient method for communicating design intent during early stages of product design, e.g., conceptual design. However, converting sketched information into precise 3-D engineering models is cumbersome, and much of this effort can be avoided by reuse of existing data. To achieve this purpose, we present a user-adaptive sketch-based retrieval method in this paper. The contributions of this work are twofold. First, we propose a statistical measure for CAD model retrieval: the measure is based on sketch similarity and accounts for users’ drawing habits. Second, for 3-D CAD models in the database, we propose a sketch generation pipeline that represents each 3-D CAD model by a small yet sufficient set of sketches that are perceptually similar to human drawings. User studies and experiments that demonstrate the effectiveness of the proposed method in the design process are presented.