**Core Concept**
The lymphatic drainage of the maxillary sinus is a critical concept in understanding the spread of maxillary carcinoma. The lymph nodes involved in the drainage of the maxillary sinus are part of the head and neck lymphatic system, which includes the submandibular, submental, and cervical lymph nodes.

**Why the Correct Answer is Right**
The first lymph node involved in maxillary carcinoma is the submandibular lymph node. This is because the lymphatic vessels from the maxillary sinus drain into the submandibular lymph nodes, which are located beneath the mandible. The submandibular lymph nodes are part of the superficial cervical lymph nodes and play a crucial role in the initial spread of cancer from the maxillary sinus.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the submental lymph nodes are involved in the drainage of the tongue, floor of the mouth, and lower lip, but not the maxillary sinus.
* **Option B:** This option is incorrect because the deep cervical lymph nodes are involved in the drainage of the neck and are not the first lymph nodes involved in maxillary carcinoma.
* **Option C:** This option is incorrect because the parotid lymph nodes are involved in the drainage of the parotid gland and are not directly related to the lymphatic drainage of the maxillary sinus.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that the lymphatic drainage of the head and neck is complex and can vary depending on the location of the tumor. The submandibular lymph nodes are often the first site of lymph node metastasis in maxillary carcinoma, highlighting the importance of including these nodes in the initial staging and treatment plan.

**Correct Answer: D. Submandibular lymph node**